Browsing by Author "Fan, Feng-lei"

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A characterization of strongly regular graphs in terms of the largest signless Laplacian eigenvalues
(2016-10-01)
Fan, Feng-lei
;
Weng, Chih-wen
;
應用數學系
;
Department of Applied Mathematics
Let G be a simple graph of order n with maximum degree Delta. Let lambda (resp. mu) denote the maximum number of common neighbors of a pair of adjacent vertices (resp. nonadjacent distinct vertices) of G. Let q(G) denote the largest eigenvalue of the signless Laplacian matrix of G. We show that q(G) <= Delta - mu/4 + root(Delta - mu/4)(2) + (1 + lambda)Delta + mu(n - 1) -Delta(2), with equality if and only if G is a strongly regular graph with parameters (n, Delta, lambda, mu). (C) 2016 Elsevier Inc. All rights
An Extending Result on Spectral Radius of Bipartite Graphs
(2018-04-01)
Cheng, Yen-Jen
;
Fan, Feng-lei
;
Weng, Chih-wen
;
應用數學系
;
Department of Applied Mathematics
In this paper, we study the spectral radius of bipartite graphs. Let G be a bipartite graph with e edges without isolated vertices. It was known that the spectral radius of G is at most the square root of e, and the upper bound is attained if and only if G is a complete bipartite graph. Suppose that G is not a complete bipartite graph and (e - 1, e + 1) is not a pair of twin primes. We describe the maximal spectral radius of G. As a byproduct of our study, we obtain a spectral characterization of a pair (e - 1, e + 1) of integers to be a pair of twin primes.