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Multicyclic treelike reflexive graphs
- Source :
-
Discrete Mathematics . Jun2005, Vol. 296 Issue 1, p43-57. 15p. - Publication Year :
- 2005
-
Abstract
- Abstract: A simple graph is reflexive if its second largest eigenvalue does not exceed 2. A graph is treelike (sometimes also called a cactus) if all its cycles (circuits) are mutually edge-disjoint. In a lot of cases one can establish whether a given graph is reflexive by identifying and removing a single cut-vertex (Theorem 1). In this paper we prove that, if this theorem cannot be applied to a connected treelike reflexive graph G and if all its cycles do not have a common vertex (do not form a bundle), such a graph has at most five cycles (Theorem 2). On the same conditions, in Theorem 3 we find all maximal treelike reflexive graphs with four and five cycles. [Copyright &y& Elsevier]
- Subjects :
- *GRAPH theory
*SUCCULENT plants
*CYCLES
*PAPER
Subjects
Details
- Language :
- English
- ISSN :
- 0012365X
- Volume :
- 296
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Discrete Mathematics
- Publication Type :
- Academic Journal
- Accession number :
- 17918779
- Full Text :
- https://doi.org/10.1016/j.disc.2005.03.007