On graphs with maximum Harary spectral radius

Fei Huang, Xueliang Li and Shujing Wang

Applied Mathematics and Computation, 2015, vol. 266, issue C, 937-945

Abstract: Let G be a connected (molecular) graph with vertex set V(G)={v1,v2,…,vn}. The Harary matrix RD(G) of G, which is also known as the reciprocal distance matrix, is an n × n matrix whose (i, j)-entry is equal to 1dij if i≠j and 0 otherwise, where dij is the distance of vi and vj in G. The spectral radius ρ(G) of the Harary matrix RD(G) has been proposed as a structure-descriptor. In this paper, we characterize graphs with maximum spectral radius of the Harary matrix in three classes of simple connected graphs with n vertices: graphs with fixed matching number, bipartite graphs with fixed matching number, and graphs with given number of cut edges, respectively.

Keywords: Harary matrix; Harary spectral radius; Matching number; Cut edge (search for similar items in EconPapers)
Date: 2015
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:266:y:2015:i:c:p:937-945

DOI: 10.1016/j.amc.2015.05.146

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