On unicycle graphs with maximum Harary spectral radius

摘要

Let G be a simple graph with vertex set V(G) = {v(1), v(2), . . . , V-n}. The Harary matrix RD(G) of G, which is initially called the reciprocal distance matrix, is an n x n matrix whose (i, j)-entry is equal to if i j and 0 otherwise, where do is the distance of and,, vi in G. Let U-n be the set of unicycle graphs and S(n, 3) be the graph obtained from the star with n vertices by adding an edge. In this paper we prove that S(n, 3) has the maximum spectral radius of Harary matrix in U-n.