On a class of tricyclic reflexive cactuses | Zendy

Bojana Mihailović | Zendy; Zoran Radosavljević | Zendy

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On a class of tricyclic reflexive cactuses

Author(s) -

Bojana Mihailović,

Zoran Radosavljević

Publication year - 2005

Publication title -

publikacija elektrotehnickog fakulteta - serija matematika

Language(s) - English

Resource type - Journals

eISSN - 2406-0852

pISSN - 0353-8893

DOI - 10.2298/petf0516055m

Subject(s) - adjacency matrix , combinatorics , vertex (graph theory) , mathematics , graph , class (philosophy) , reflexivity , reciprocal , discrete mathematics , computer science , sociology , philosophy , social science , linguistics , artificial intelligence

A simple graph is reflexive if the second largest eigenvalue of its (0, 1) adjacency matrix does not exceed 2. A graph is a cactus, or a treelike graph, if any pair of its cycles (circuits) has at most one common vertex. The subject of this paper is the class of tricyclic cactuses in which the central cycle is a quadrangle touching the rest two cycles at its non-adjacent vertices. In this class we describe a set of maximal reflexive graphs. The so-called “pouring” of Smith trees plays the crucial role in characterizing the resulting set.

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