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1. Performance Comparisons of Self-stabilizing Algorithms for Maximal Independent Sets

Author

Cone, Barton F., Hedetniemi, Stephen T., Ingle, Lance C., and Kennedy, Ken

Subjects
Computer Science - Distributed, Parallel, and Cluster Computing
Abstract

Sensor networks, such as ultra-wideband sensors for the smart warehouse, may need to run distributed algorithms for automatically determining a topological layout. In this paper, we present 5 different self-stabilizing algorithms (their central and distributed counterparts) for determining maximal independent sets. The performance of the algorithms, in terms of time complexity, simulation analysis, and size of maximal independent sets found are then compared., Comment: 8 pages

Published
2022

2. Fundamentals of Domination

Author

Haynes, Teresa W., Hedetniemi, Stephen T., Henning, Michael A., Kim, Minhyong, Editor-in-Chief, Wendland, Katrin, Editor-in-Chief, Axler, Sheldon, Series Editor, Braverman, Mark, Series Editor, Chudnovsky, Maria, Series Editor, Funaki, Tadahisa, Series Editor, Gallagher, Isabelle, Series Editor, Güntürk, Sinan, Series Editor, Le Bris, Claude, Series Editor, Massart, Pascal, Series Editor, Pinto, Alberto A., Series Editor, Pinzari, Gabriella, Series Editor, Ribet, Ken, Series Editor, Schilling, René, Series Editor, Souganidis, Panagiotis, Series Editor, Süli, Endre, Series Editor, Weinberger, Shmuel, Series Editor, Zilber, Boris, Series Editor, Haynes, Teresa W., Hedetniemi, Stephen T., and Henning, Michael A.

Published
2023
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3. Domination in Trees

Author

Haynes, Teresa W., Hedetniemi, Stephen T., Henning, Michael A., Kim, Minhyong, Editor-in-Chief, Wendland, Katrin, Editor-in-Chief, Axler, Sheldon, Series Editor, Braverman, Mark, Series Editor, Chudnovsky, Maria, Series Editor, Funaki, Tadahisa, Series Editor, Gallagher, Isabelle, Series Editor, Güntürk, Sinan, Series Editor, Le Bris, Claude, Series Editor, Massart, Pascal, Series Editor, Pinto, Alberto A., Series Editor, Pinzari, Gabriella, Series Editor, Ribet, Ken, Series Editor, Schilling, René, Series Editor, Souganidis, Panagiotis, Series Editor, Süli, Endre, Series Editor, Weinberger, Shmuel, Series Editor, Zilber, Boris, Series Editor, Haynes, Teresa W., Hedetniemi, Stephen T., and Henning, Michael A.

Published
2023
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4. Complexity and Algorithms for Domination in Graphs

Author

Haynes, Teresa W., Hedetniemi, Stephen T., Henning, Michael A., Kim, Minhyong, Editor-in-Chief, Wendland, Katrin, Editor-in-Chief, Axler, Sheldon, Series Editor, Braverman, Mark, Series Editor, Chudnovsky, Maria, Series Editor, Funaki, Tadahisa, Series Editor, Gallagher, Isabelle, Series Editor, Güntürk, Sinan, Series Editor, Le Bris, Claude, Series Editor, Massart, Pascal, Series Editor, Pinto, Alberto A., Series Editor, Pinzari, Gabriella, Series Editor, Ribet, Ken, Series Editor, Schilling, René, Series Editor, Souganidis, Panagiotis, Series Editor, Süli, Endre, Series Editor, Weinberger, Shmuel, Series Editor, Zilber, Boris, Series Editor, Haynes, Teresa W., Hedetniemi, Stephen T., and Henning, Michael A.

Published
2023
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5. Efficient Domination in Graphs

Author

Haynes, Teresa W., Hedetniemi, Stephen T., Henning, Michael A., Kim, Minhyong, Editor-in-Chief, Wendland, Katrin, Editor-in-Chief, Axler, Sheldon, Series Editor, Braverman, Mark, Series Editor, Chudnovsky, Maria, Series Editor, Funaki, Tadahisa, Series Editor, Gallagher, Isabelle, Series Editor, Güntürk, Sinan, Series Editor, Le Bris, Claude, Series Editor, Massart, Pascal, Series Editor, Pinto, Alberto A., Series Editor, Pinzari, Gabriella, Series Editor, Ribet, Ken, Series Editor, Schilling, René, Series Editor, Souganidis, Panagiotis, Series Editor, Süli, Endre, Series Editor, Weinberger, Shmuel, Series Editor, Zilber, Boris, Series Editor, Haynes, Teresa W., Hedetniemi, Stephen T., and Henning, Michael A.

Published
2023
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6. General Bounds

Author

Haynes, Teresa W., Hedetniemi, Stephen T., Henning, Michael A., Kim, Minhyong, Editor-in-Chief, Wendland, Katrin, Editor-in-Chief, Axler, Sheldon, Series Editor, Braverman, Mark, Series Editor, Chudnovsky, Maria, Series Editor, Funaki, Tadahisa, Series Editor, Gallagher, Isabelle, Series Editor, Güntürk, Sinan, Series Editor, Le Bris, Claude, Series Editor, Massart, Pascal, Series Editor, Pinto, Alberto A., Series Editor, Pinzari, Gabriella, Series Editor, Ribet, Ken, Series Editor, Schilling, René, Series Editor, Souganidis, Panagiotis, Series Editor, Süli, Endre, Series Editor, Weinberger, Shmuel, Series Editor, Zilber, Boris, Series Editor, Haynes, Teresa W., Hedetniemi, Stephen T., and Henning, Michael A.

Published
2023
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7. Bounds in Terms of Size

Author

Haynes, Teresa W., Hedetniemi, Stephen T., Henning, Michael A., Kim, Minhyong, Editor-in-Chief, Wendland, Katrin, Editor-in-Chief, Axler, Sheldon, Series Editor, Braverman, Mark, Series Editor, Chudnovsky, Maria, Series Editor, Funaki, Tadahisa, Series Editor, Gallagher, Isabelle, Series Editor, Güntürk, Sinan, Series Editor, Le Bris, Claude, Series Editor, Massart, Pascal, Series Editor, Pinto, Alberto A., Series Editor, Pinzari, Gabriella, Series Editor, Ribet, Ken, Series Editor, Schilling, René, Series Editor, Souganidis, Panagiotis, Series Editor, Süli, Endre, Series Editor, Weinberger, Shmuel, Series Editor, Zilber, Boris, Series Editor, Haynes, Teresa W., Hedetniemi, Stephen T., and Henning, Michael A.

Published
2023
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8. Probabilistic Bounds and Domination in Random Graphs

Author

Haynes, Teresa W., Hedetniemi, Stephen T., Henning, Michael A., Kim, Minhyong, Editor-in-Chief, Wendland, Katrin, Editor-in-Chief, Axler, Sheldon, Series Editor, Braverman, Mark, Series Editor, Chudnovsky, Maria, Series Editor, Funaki, Tadahisa, Series Editor, Gallagher, Isabelle, Series Editor, Güntürk, Sinan, Series Editor, Le Bris, Claude, Series Editor, Massart, Pascal, Series Editor, Pinto, Alberto A., Series Editor, Pinzari, Gabriella, Series Editor, Ribet, Ken, Series Editor, Schilling, René, Series Editor, Souganidis, Panagiotis, Series Editor, Süli, Endre, Series Editor, Weinberger, Shmuel, Series Editor, Zilber, Boris, Series Editor, Haynes, Teresa W., Hedetniemi, Stephen T., and Henning, Michael A.

Published
2023
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9. Upper Bounds in Terms of Minimum Degree

Author

Haynes, Teresa W., Hedetniemi, Stephen T., Henning, Michael A., Kim, Minhyong, Editor-in-Chief, Wendland, Katrin, Editor-in-Chief, Axler, Sheldon, Series Editor, Braverman, Mark, Series Editor, Chudnovsky, Maria, Series Editor, Funaki, Tadahisa, Series Editor, Gallagher, Isabelle, Series Editor, Güntürk, Sinan, Series Editor, Le Bris, Claude, Series Editor, Massart, Pascal, Series Editor, Pinto, Alberto A., Series Editor, Pinzari, Gabriella, Series Editor, Ribet, Ken, Series Editor, Schilling, René, Series Editor, Souganidis, Panagiotis, Series Editor, Süli, Endre, Series Editor, Weinberger, Shmuel, Series Editor, Zilber, Boris, Series Editor, Haynes, Teresa W., Hedetniemi, Stephen T., and Henning, Michael A.

Published
2023
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10. Domination Critical and Stable Graphs

Author

Haynes, Teresa W., Hedetniemi, Stephen T., Henning, Michael A., Kim, Minhyong, Editor-in-Chief, Wendland, Katrin, Editor-in-Chief, Axler, Sheldon, Series Editor, Braverman, Mark, Series Editor, Chudnovsky, Maria, Series Editor, Funaki, Tadahisa, Series Editor, Gallagher, Isabelle, Series Editor, Güntürk, Sinan, Series Editor, Le Bris, Claude, Series Editor, Massart, Pascal, Series Editor, Pinto, Alberto A., Series Editor, Pinzari, Gabriella, Series Editor, Ribet, Ken, Series Editor, Schilling, René, Series Editor, Souganidis, Panagiotis, Series Editor, Süli, Endre, Series Editor, Weinberger, Shmuel, Series Editor, Zilber, Boris, Series Editor, Haynes, Teresa W., Hedetniemi, Stephen T., and Henning, Michael A.

Published
2023
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11. Domination and Vizing’s Conjecture

Author

Haynes, Teresa W., Hedetniemi, Stephen T., Henning, Michael A., Kim, Minhyong, Editor-in-Chief, Wendland, Katrin, Editor-in-Chief, Axler, Sheldon, Series Editor, Braverman, Mark, Series Editor, Chudnovsky, Maria, Series Editor, Funaki, Tadahisa, Series Editor, Gallagher, Isabelle, Series Editor, Güntürk, Sinan, Series Editor, Le Bris, Claude, Series Editor, Massart, Pascal, Series Editor, Pinto, Alberto A., Series Editor, Pinzari, Gabriella, Series Editor, Ribet, Ken, Series Editor, Schilling, René, Series Editor, Souganidis, Panagiotis, Series Editor, Süli, Endre, Series Editor, Weinberger, Shmuel, Series Editor, Zilber, Boris, Series Editor, Haynes, Teresa W., Hedetniemi, Stephen T., and Henning, Michael A.

Published
2023
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12. In The Beginning: Roots of Domination in Graphs

Author

Haynes, Teresa W., Hedetniemi, Stephen T., Henning, Michael A., Kim, Minhyong, Editor-in-Chief, Wendland, Katrin, Editor-in-Chief, Axler, Sheldon, Series Editor, Braverman, Mark, Series Editor, Chudnovsky, Maria, Series Editor, Funaki, Tadahisa, Series Editor, Gallagher, Isabelle, Series Editor, Güntürk, Sinan, Series Editor, Le Bris, Claude, Series Editor, Massart, Pascal, Series Editor, Pinto, Alberto A., Series Editor, Pinzari, Gabriella, Series Editor, Ribet, Ken, Series Editor, Schilling, René, Series Editor, Souganidis, Panagiotis, Series Editor, Süli, Endre, Series Editor, Weinberger, Shmuel, Series Editor, Zilber, Boris, Series Editor, Haynes, Teresa W., Hedetniemi, Stephen T., and Henning, Michael A.

Published
2023
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13. Domination in Grids and Hypercubes

Author

Haynes, Teresa W., Hedetniemi, Stephen T., Henning, Michael A., Kim, Minhyong, Editor-in-Chief, Wendland, Katrin, Editor-in-Chief, Axler, Sheldon, Series Editor, Braverman, Mark, Series Editor, Chudnovsky, Maria, Series Editor, Funaki, Tadahisa, Series Editor, Gallagher, Isabelle, Series Editor, Güntürk, Sinan, Series Editor, Le Bris, Claude, Series Editor, Massart, Pascal, Series Editor, Pinto, Alberto A., Series Editor, Pinzari, Gabriella, Series Editor, Ribet, Ken, Series Editor, Schilling, René, Series Editor, Souganidis, Panagiotis, Series Editor, Süli, Endre, Series Editor, Weinberger, Shmuel, Series Editor, Zilber, Boris, Series Editor, Haynes, Teresa W., Hedetniemi, Stephen T., and Henning, Michael A.

Published
2023
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14. Nordhaus-Gaddum Bounds

Author

Haynes, Teresa W., Hedetniemi, Stephen T., Henning, Michael A., Kim, Minhyong, Editor-in-Chief, Wendland, Katrin, Editor-in-Chief, Axler, Sheldon, Series Editor, Braverman, Mark, Series Editor, Chudnovsky, Maria, Series Editor, Funaki, Tadahisa, Series Editor, Gallagher, Isabelle, Series Editor, Güntürk, Sinan, Series Editor, Le Bris, Claude, Series Editor, Massart, Pascal, Series Editor, Pinto, Alberto A., Series Editor, Pinzari, Gabriella, Series Editor, Ribet, Ken, Series Editor, Schilling, René, Series Editor, Souganidis, Panagiotis, Series Editor, Süli, Endre, Series Editor, Weinberger, Shmuel, Series Editor, Zilber, Boris, Series Editor, Haynes, Teresa W., Hedetniemi, Stephen T., and Henning, Michael A.

Published
2023
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15. Upper Domination Parameters

Author

Haynes, Teresa W., Hedetniemi, Stephen T., Henning, Michael A., Kim, Minhyong, Editor-in-Chief, Wendland, Katrin, Editor-in-Chief, Axler, Sheldon, Series Editor, Braverman, Mark, Series Editor, Chudnovsky, Maria, Series Editor, Funaki, Tadahisa, Series Editor, Gallagher, Isabelle, Series Editor, Güntürk, Sinan, Series Editor, Le Bris, Claude, Series Editor, Massart, Pascal, Series Editor, Pinto, Alberto A., Series Editor, Pinzari, Gabriella, Series Editor, Ribet, Ken, Series Editor, Schilling, René, Series Editor, Souganidis, Panagiotis, Series Editor, Süli, Endre, Series Editor, Weinberger, Shmuel, Series Editor, Zilber, Boris, Series Editor, Haynes, Teresa W., Hedetniemi, Stephen T., and Henning, Michael A.

Published
2023
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16. Relating the Core Parameters

Author

Haynes, Teresa W., Hedetniemi, Stephen T., Henning, Michael A., Kim, Minhyong, Editor-in-Chief, Wendland, Katrin, Editor-in-Chief, Axler, Sheldon, Series Editor, Braverman, Mark, Series Editor, Chudnovsky, Maria, Series Editor, Funaki, Tadahisa, Series Editor, Gallagher, Isabelle, Series Editor, Güntürk, Sinan, Series Editor, Le Bris, Claude, Series Editor, Massart, Pascal, Series Editor, Pinto, Alberto A., Series Editor, Pinzari, Gabriella, Series Editor, Ribet, Ken, Series Editor, Schilling, René, Series Editor, Souganidis, Panagiotis, Series Editor, Süli, Endre, Series Editor, Weinberger, Shmuel, Series Editor, Zilber, Boris, Series Editor, Haynes, Teresa W., Hedetniemi, Stephen T., and Henning, Michael A.

Published
2023
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17. Domination and Forbidden Subgraphs

Author

Haynes, Teresa W., Hedetniemi, Stephen T., Henning, Michael A., Kim, Minhyong, Editor-in-Chief, Wendland, Katrin, Editor-in-Chief, Axler, Sheldon, Series Editor, Braverman, Mark, Series Editor, Chudnovsky, Maria, Series Editor, Funaki, Tadahisa, Series Editor, Gallagher, Isabelle, Series Editor, Güntürk, Sinan, Series Editor, Le Bris, Claude, Series Editor, Massart, Pascal, Series Editor, Pinto, Alberto A., Series Editor, Pinzari, Gabriella, Series Editor, Ribet, Ken, Series Editor, Schilling, René, Series Editor, Souganidis, Panagiotis, Series Editor, Süli, Endre, Series Editor, Weinberger, Shmuel, Series Editor, Zilber, Boris, Series Editor, Haynes, Teresa W., Hedetniemi, Stephen T., and Henning, Michael A.

Published
2023
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18. Dominating Partitions

Author

Haynes, Teresa W., Hedetniemi, Stephen T., Henning, Michael A., Kim, Minhyong, Editor-in-Chief, Wendland, Katrin, Editor-in-Chief, Axler, Sheldon, Series Editor, Braverman, Mark, Series Editor, Chudnovsky, Maria, Series Editor, Funaki, Tadahisa, Series Editor, Gallagher, Isabelle, Series Editor, Güntürk, Sinan, Series Editor, Le Bris, Claude, Series Editor, Massart, Pascal, Series Editor, Pinto, Alberto A., Series Editor, Pinzari, Gabriella, Series Editor, Ribet, Ken, Series Editor, Schilling, René, Series Editor, Souganidis, Panagiotis, Series Editor, Süli, Endre, Series Editor, Weinberger, Shmuel, Series Editor, Zilber, Boris, Series Editor, Haynes, Teresa W., Hedetniemi, Stephen T., and Henning, Michael A.

Published
2023
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19. Domination in Planar Graphs

Author

Haynes, Teresa W., Hedetniemi, Stephen T., Henning, Michael A., Kim, Minhyong, Editor-in-Chief, Wendland, Katrin, Editor-in-Chief, Axler, Sheldon, Series Editor, Braverman, Mark, Series Editor, Chudnovsky, Maria, Series Editor, Funaki, Tadahisa, Series Editor, Gallagher, Isabelle, Series Editor, Güntürk, Sinan, Series Editor, Le Bris, Claude, Series Editor, Massart, Pascal, Series Editor, Pinto, Alberto A., Series Editor, Pinzari, Gabriella, Series Editor, Ribet, Ken, Series Editor, Schilling, René, Series Editor, Souganidis, Panagiotis, Series Editor, Süli, Endre, Series Editor, Weinberger, Shmuel, Series Editor, Zilber, Boris, Series Editor, Haynes, Teresa W., Hedetniemi, Stephen T., and Henning, Michael A.

Published
2023
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22. Self-Stabilizing Domination Algorithms

Author

Hedetniemi, Stephen T., Alladi, Krishnaswami, Series Editor, Tiep, Pham Huu, Series Editor, Tu, Loring W., Series Editor, Haynes, Teresa W., editor, Hedetniemi, Stephen T., editor, and Henning, Michael A., editor

Published
2021
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24. Domination in Digraphs

Author

Haynes, Teresa W., Hedetniemi, Stephen T., Henning, Michael A., Alladi, Krishnaswami, Series Editor, Tiep, Pham Huu, Series Editor, Tu, Loring W., Series Editor, Haynes, Teresa W., editor, Hedetniemi, Stephen T., editor, and Henning, Michael A., editor

Published
2021
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26. Domination in Chessboards

Author

Hedetniemi, Jason T., Hedetniemi, Stephen T., Alladi, Krishnaswami, Series Editor, Tiep, Pham Huu, Series Editor, Tu, Loring W., Series Editor, Haynes, Teresa W., editor, Hedetniemi, Stephen T., editor, and Henning, Michael A., editor

Published
2021
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27. The Private Neighbor Concept

Author

Hedetniemi, Stephen T., McRae, Alice A., Mohan, Raghuveer, Alladi, Krishnaswami, Series Editor, Tiep, Pham Huu, Series Editor, Tu, Loring W., Series Editor, Haynes, Teresa W., editor, Hedetniemi, Stephen T., editor, and Henning, Michael A., editor

Published
2021
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28. Alliances and Related Domination Parameters

Author

Haynes, Teresa W., Hedetniemi, Stephen T., Alladi, Krishnaswami, Series Editor, Tiep, Pham Huu, Series Editor, Tu, Loring W., Series Editor, Haynes, Teresa W., editor, Hedetniemi, Stephen T., editor, and Henning, Michael A., editor

Published
2021
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29. Glossary of Common Terms

Author

Haynes, Teresa W., Hedetniemi, Stephen T., Henning, Michael A., Alladi, Krishnaswami, Series Editor, Tiep, Pham Huu, Series Editor, Tu, Loring W., Series Editor, Haynes, Teresa W., editor, Hedetniemi, Stephen T., editor, and Henning, Michael A., editor

Published
2021
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30. Offensive Alliances in Graphs

Author

Favaron, Odile, primary, Fricke, Gerd, additional, Goddard*, Wayne, additional, Hedetniemi, Sandra M., additional, Hedetniemi, Stephen T., additional, Kristiansen, Petter, additional, Laskar, Renu C., additional, and Skaggs, Duane, additional

Published
2022
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33. Models of Domination in Graphs

Author

Haynes, Teresa W., Hedetniemi, Stephen T., Henning, Michael A., Alladi, Krishnaswami, Series Editor, Tiep, Pham Huu, Series Editor, Tu, Loring W., Series Editor, Haynes, Teresa W., editor, Hedetniemi, Stephen T., editor, and Henning, Michael A., editor

Published
2020
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34. Glossary of Common Terms

Author

Haynes, Teresa W., Hedetniemi, Stephen T., Henning, Michael A., Alladi, Krishnaswami, Series Editor, Tiep, Pham Huu, Series Editor, Tu, Loring W., Series Editor, Haynes, Teresa W., editor, Hedetniemi, Stephen T., editor, and Henning, Michael A., editor

Published
2020
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35. Partial Domination in Graphs

Author

Case, Benjamin M., Hedetniemi, Stephen T., Laskar, Renu C., and Lipman, Drew J.

Subjects
Mathematics - Combinatorics
Abstract

A set $S\subseteq V$ is a dominating set of $G$ if every vertex in $V - S$ is adjacent to at least one vertex in $S$. The domination number $\gamma(G)$ of $G$ equals the minimum cardinality of a dominating set $S$ in $G$; we say that such a set $S$ is a $\gamma$-set. The single greatest focus of research in domination theory is the determination of the value of $\gamma(G)$. By definition, all vertices must be dominated by a $\gamma$-set. In this paper we propose relaxing this requirement, by seeking sets of vertices that dominate a prescribed fraction of the vertices of a graph. We focus particular attention on $1/2$ domination, that is, sets of vertices that dominate at least half of the vertices of a graph $G$. Keywords: partial domination, dominating set, partial domination number, domination number, Comment: First presented at the 48th Southeastern International Conference on Combinatorics, Graph Theory & Computing March 6-10, 2017

Published
2017

36. Ulam Numbers of Graphs

Author

Hedetniemi, Stephen T., Winkler, Peter, Series Editor, Gera, Ralucca, editor, Haynes, Teresa W., editor, and Hedetniemi, Stephen T., editor

Published
2018
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37. Introduction

Author

Gera, Ralucca, Hedetniemi, Stephen T., Haynes, Teresa W., Winkler, Peter, Series Editor, Gera, Ralucca, editor, Haynes, Teresa W., editor, and Hedetniemi, Stephen T., editor

Published
2018
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47. Rainbow Disconnection in Graphs

Author

Chartrand Gary, Devereaux Stephen, Haynes Teresa W., Hedetniemi Stephen T., and Zhang Ping

Subjects
edge coloring, rainbow connection, rainbow disconnection, 05c15, 05c40, Mathematics, QA1-939
Abstract

Let G be a nontrivial connected, edge-colored graph. An edge-cut R of G is called a rainbow cut if no two edges in R are colored the same. An edge-coloring of G is a rainbow disconnection coloring if for every two distinct vertices u and v of G, there exists a rainbow cut in G, where u and v belong to different components of G − R. We introduce and study the rainbow disconnection number rd(G) of G, which is defined as the minimum number of colors required of a rainbow disconnection coloring of G. It is shown that the rainbow disconnection number of a nontrivial connected graph G equals the maximum rainbow disconnection number among the blocks of G. It is also shown that for a nontrivial connected graph G of order n, rd(G) = n−1 if and only if G contains at least two vertices of degree n − 1. The rainbow disconnection numbers of all grids Pm _ Pn are determined. Furthermore, it is shown for integers k and n with 1 ≤ k ≤ n − 1 that the minimum size of a connected graph of order n having rainbow disconnection number k is n + k − 2. Other results and a conjecture are also presented.

Published
2018
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