Browsing by Author "Liu, Chia-an"

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Spectral radius and degree sequence of a graph
(2013-04-15)
Liu, Chia-an
;
Weng, Chih-wen
;
應用數學系
;
Department of Applied Mathematics
Let G be a simple connected graph of order n with degree sequence d(1), d(2), ... , dr, in non-increasing, order. The spectral radius rho(G) of G is the largest eigenvalue of its adjacency matrix. For each positive integer l at most n, we give a sharp upper bound for rho(G) by a function of d(1), d(2), ... ,d(l), which generalizes a series of previous results. (C) 2013 Elsevier Inc. All rights reserved.
Spectral radius of bipartite graphs
(2015-06-01)
Liu, Chia-an
;
Weng, Chih-wen
;
應用數學系
;
Department of Applied Mathematics
Let k, p, q be positive integers with k < p < q + 1. We prove that the maximum spectral radius of a simple bipartite graph obtained from the complete bipartite graph K-p,K-q of bipartition orders p and q by deleting k edges is attained when the deleted edges are all incident on a common vertex which is located in the partite set of order q. Our method is based on new sharp upper bounds on the spectral radius of bipartite graphs in terms of their degree sequences. (C) 2015 Elsevier Inc. All rights reserved.