Affiliation:
1. Federal University of Rio de Janeiro, Brazil
2. Federal Fluminense University, Instituto de Cincias Exatas, Departamento de Matematica, Desembargador Ellis Hermydio F, Brazil
3. CEFET-RJ, Brazil
4. ENCE, Brazil
Abstract
Let G be a graph on n vertices and G? its complement. In this paper, we prove
a Nordhaus-Gaddum type inequality to the second largest eigenvalue of a graph
G, ?2(G), ?2(G) + ?2(G?) ? -1 + ? n2/2-n+1, when G is a graph with girth
at least 5. Also, we show that the bound above is tight. Besides, we prove
that this result holds for some classes of connected graphs such as trees,
k-cyclic, regular bipartite and complete multipartite graphs. Based on these
facts, we conjecture that our result holds to any graph.
Publisher
National Library of Serbia
Subject
Applied Mathematics,Discrete Mathematics and Combinatorics,Analysis
Cited by
4 articles.
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