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On the same conditions, in Theorem 3 we find all maximal treelike reflexive graphs with four and five cycles. ... 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. ... Acknowledgements Getting these results has been facilitated by making use of the expert system GRAPH  . ...doi:10.1016/j.disc.2005.03.007 fatcat:wd4n6463vvhlbcauaoqbm5uxgq
Rasˇajski Multicyclic treelike reflexive graphs 43 N.D. Tan and L.X. Hung On the Burkard-Hammer condition for hamiltonian split graphs 59 T. ... Wu On directed zero-divisor graphs of finite rings 73 X. Zhang Compatibly ordered-OSTS of order n and compatibly ordered-OGDD of type h n for n ¼ 6k þ 1 8 7 I. ...doi:10.1016/s0012-365x(05)00207-4 fatcat:qp7apuodx5chhecbryeorys7hi
A graph is a cactus, or a treelike graph, if any pair of its cycles (circuits) has at most one common vertex. ... In this class we describe a set of maximal reflexive graphs. ... The work on this project has been facilitated by making use of the programming package GRAPH  . ...doi:10.2298/petf0516055m fatcat:mf6pqtofkfepfp5qwadljuvz7m
Cacti, or treelike graphs, are graphs whose all cycles are mutually edge-disjoint. ... The property λ 2 2 is a hereditary one, i.e. all induced subgraphs of a reflexive graph are also reflexive. ... Acknowledgements We used the expert system newGRAPH  for computations of eigenvalues of graphs. ...doi:10.1016/j.laa.2011.04.023 fatcat:f4z4flwotfhdfgxohueskm7mky
We use graph modifications involving Smith trees to construct four classes of maximal bicyclic reflexive graphs. ... A simple graph is said to be reflexive if the second largest eigenvalue of a (0, 1)-adjacency matrix does not exceed 2. ... Acknowledgements The work on this article, including the related former results of these authors, has been facilitated by the programming package GRAPH  . ...doi:10.1016/j.disc.2007.07.057 fatcat:zm6xbotqt5f3dedr44d2rnopfm