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Your search keyword '"Adjacency matrix"' showing total 6 results
6 results on '"Adjacency matrix"'

1. On unicyclic non-bipartite graphs with tricyclic inverses.

Author

Kalita, Debajit and Sarma, Kuldeep

Subjects
*BIPARTITE graphs
Abstract

The class of unicyclic non-bipartite graphs with unique perfect matching, denoted by U , is considered in this article. This article provides a complete characterization of unicyclic graphs in U which possess tricyclic inverses. [ABSTRACT FROM AUTHOR]

Published
2023
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2. Inverses of non-bipartite unicyclic graphs with a unique perfect matching.

Author

Kalita, Debajit and Sarma, Kuldeep

Subjects
*MATRIX inversion, *CHARTS, diagrams, etc.
Abstract

The class of non-bipartite unicyclic graphs with a unique perfect matching, denoted by U , is considered in this article. This article describes the entries of the inverse of the adjacency matrix of a graph in U . It is proved that the inverse graph of a graph in U is always non-bipartite. In this article, we characterize the graphs in U whose inverses are mixed graphs. Among all such graphs in U we identify those graphs whose inverses are quasi-bipartite. Furthermore, characterizations of unicyclic graphs in U possessing unicyclic and bicyclic inverses are also provided in this article. [ABSTRACT FROM AUTHOR]

Published
2022
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3. A new algorithm to find fuzzy Hamilton cycle in a fuzzy network using adjacency matrix and minimum vertex degree.

Author

Nagoor Gani, A. and Latha, S.

Subjects
*GEOMETRIC vertices, *HAMILTON'S principle function, *HAMILTONIAN mechanics, *HAMILTON'S equations, *ALGORITHMS, *MATHEMATICAL programming
Abstract

A Hamiltonian cycle in a graph is a cycle that visits each node/vertex exactly once. A graph containing a Hamiltonian cycle is called a Hamiltonian graph. There have been several researches to find the number of Hamiltonian cycles of a Hamilton graph. As the number of vertices and edges grow, it becomes very difficult to keep track of all the different ways through which the vertices are connected. Hence, analysis of large graphs can be efficiently done with the assistance of a computer system that interprets graphs as matrices. And, of course, a good and well written algorithm will expedite the analysis even faster. The most convenient way to quickly test whether there is an edge between two vertices is to represent graphs using adjacent matrices. In this paper, a new algorithm is proposed to find fuzzy Hamiltonian cycle using adjacency matrix and the degree of the vertices of a fuzzy graph. A fuzzy graph structure is also modeled to illustrate the proposed algorithms with the selected air network of Indigo airlines. [ABSTRACT FROM AUTHOR]

Published
2016
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4. Spectral conditions for the existence of specified paths and cycles in graphs.

Author

Zhai, Mingqing, Lin, Huiqiu, and Gong, Shicai

Subjects
*EXISTENCE theorems, *PATH analysis (Statistics), *CYCLIC groups, *EIGENVALUES, *LEAST squares
Abstract

Let G be a graph with n vertices and λ n ( G ) be the least eigenvalue of its adjacency matrix of G . In this paper, we give sharp bounds on the least eigenvalue of graphs without given paths or cycles and determine the extremal graphs. This result gives spectral conditions for the existence of specified paths and cycles in graphs. [ABSTRACT FROM AUTHOR]

Published
2015
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5. A new algorithm to find fuzzy Hamilton cycle in a fuzzy network using adjacency matrix and minimum vertex degree

Author

S. Latha and A. Nagoor Gani

Subjects
Fuzzy Hamiltonian cycle, Computer science, 0102 computer and information sciences, 01 natural sciences, symbols.namesake, Graph power, Degree of a vertex in a fuzzy graph, Wheel graph, 05C85, Adjacency matrix, 0101 mathematics, Multidisciplinary, Research, 010102 general mathematics, Fuzzy graph, Neighbourhood (graph theory), Hamiltonian path, Hypercube graph, 05C38, 010201 computation theory & mathematics, Fuzzy Hamiltonian path, symbols, Adjacency list, Regular graph, 05C72, Algorithm, MathematicsofComputing_DISCRETEMATHEMATICS
Abstract

A Hamiltonian cycle in a graph is a cycle that visits each node/vertex exactly once. A graph containing a Hamiltonian cycle is called a Hamiltonian graph. There have been several researches to find the number of Hamiltonian cycles of a Hamilton graph. As the number of vertices and edges grow, it becomes very difficult to keep track of all the different ways through which the vertices are connected. Hence, analysis of large graphs can be efficiently done with the assistance of a computer system that interprets graphs as matrices. And, of course, a good and well written algorithm will expedite the analysis even faster. The most convenient way to quickly test whether there is an edge between two vertices is to represent graphs using adjacent matrices. In this paper, a new algorithm is proposed to find fuzzy Hamiltonian cycle using adjacency matrix and the degree of the vertices of a fuzzy graph. A fuzzy graph structure is also modeled to illustrate the proposed algorithms with the selected air network of Indigo airlines.

Published
2016

6. Nilpotent adjacency matrices, random graphs, and quantum random variables

Author

George Stacey Staples, René Schott, Institut Élie Cartan de Nancy (IECN), Centre National de la Recherche Scientifique (CNRS)-Institut National Polytechnique de Lorraine (INPL)-Université Nancy 2-Université Henri Poincaré - Nancy 1 (UHP)-Institut National de Recherche en Informatique et en Automatique (Inria), Laboratoire Lorrain de Recherche en Informatique et ses Applications (LORIA), Centre National de la Recherche Scientifique (CNRS)-Université de Lorraine (UL)-Institut National de Recherche en Informatique et en Automatique (Inria), Department of Mathematics and Statistics - Southern Illinois University, Southern Illinois University [Edwardsville] (SIUE), Schott, René, Institut National de Recherche en Informatique et en Automatique (Inria)-Université Henri Poincaré - Nancy 1 (UHP)-Université Nancy 2-Institut National Polytechnique de Lorraine (INPL)-Centre National de la Recherche Scientifique (CNRS), and Institut National de Recherche en Informatique et en Automatique (Inria)-Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Statistics and Probability, [MATH.MATH-PR] Mathematics [math]/Probability [math.PR], paths, General Physics and Astronomy, cycles, 01 natural sciences, quantum computing, Combinatorics, 0103 physical sciences, fermions, Adjacency matrix, 0101 mathematics, Abelian group, Algebraic number, Mathematical Physics, random graphs, Mathematics, Random graph, Discrete mathematics, 60B99, 81P68, 05C38, 05C50, 05C80, 15A66, 010102 general mathematics, Subalgebra, Statistical and Nonlinear Physics, Matrix multiplication, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], Nilpotent, Modeling and Simulation, 010307 mathematical physics, Random variable
Abstract

International audience; For fixed $n>0$, the space of finite graphs on $n$ vertices is canonically associated with an abelian, nilpotent-generated subalgebra of the $2n$-particle fermion algebra. using the generators of the subalgebra, an algebraic probability space of "nilpotent adjacency matrices" associated with finite graphs is defined. Each nilpotent adjacency matrix is a quantum random variable whose $m^th$ moment corresponds to the number of $m$-cycles in the graph $G$. Each matrix admits a canonical "quantum decomposition" into a sum of three algebraic random variables: $a = a^\Delta+ a^\Upsilon+a^Lambda$, where $a^\Delta$ is classical while $a^\Upsilon and $a^\Lambda$ are quantum. Moreover, within the algebraic context, the NP problem of cycle enumeration is reduced to matrix multiplication, requiring no more than $n^4$ multiplications within the algebra.

Published
2008

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