Browsing by Author "Cheng, Yen-Jen"

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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.