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Multicyclic treelike reflexive graphs

Z. Radosavljević, M. Rašajski
2005 Discrete Mathematics  
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 [2] .  ... 
doi:10.1016/j.disc.2005.03.007 fatcat:wd4n6463vvhlbcauaoqbm5uxgq

Contents

2005 Discrete Mathematics  
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

On a class of tricyclic reflexive cactuses

Bojana Mihailovic, Zoran Radosavljevic
2005 Publikacija Elektrotehnickog fakulteta - serija matematika  
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 [2] .  ... 
doi:10.2298/petf0516055m fatcat:mf6pqtofkfepfp5qwadljuvz7m

Maximal reflexive cacti with four cycles: The approach via Smith graphs

M. Rašajski, Z. Radosavljević, B. Mihailović
2011 Linear Algebra and its Applications  
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 [22] for computations of eigenvalues of graphs.  ... 
doi:10.1016/j.laa.2011.04.023 fatcat:f4z4flwotfhdfgxohueskm7mky

On bicyclic reflexive graphs

Zoran Radosavljević, Bojana Mihailović, Marija Rašajski
2008 Discrete Mathematics  
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 [2] .  ... 
doi:10.1016/j.disc.2007.07.057 fatcat:zm6xbotqt5f3dedr44d2rnopfm