1. Multicyclic treelike reflexive graphs
- Author
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Radosavljević, Z. and Rašajski, M.
- Subjects
- *
GRAPH theory , *SUCCULENT plants , *CYCLES , *PAPER - 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]
- Published
- 2005
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