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Laplacian eigenvalue distribution and graph parameters
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NSTL
Elsevier
Let G be a graph and I be an interval. In this paper, we present bounds for the number mGI of Laplacian eigenvalues in I in terms of structural parameters of G. In particular, we show that mG(n?α(G),n]≤n?α(G) and mG(n?d(G)+3,n]≤n?d(G)?1, where α(G) and d(G) denote the independence number and the diameter of G, respectively. Also, we characterize bipartite graphs that satisfy mG[0,1)=α(G). Further, in the case of triangle-free or quadrangle-free, we prove that mG(n?1,n]≤1.
Laplacian eigenvalue
Ahanjideh M.、Akbari S.、Fakharan M.H.、Trevisan V.
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Department of Industrial Engineering Bo?azi?i University
Department of Mathematical Sciences Sharif University of Technology
NSTL
Elsevier
