Some spectral bounds for the harmonic matrix
نویسندگان
چکیده
The aim of this note is to establish new spectral bounds for the harmonic matrix. The Harary matrix of given a connected graph G of order n, say RD(G), is an n-by-n symmetric matrix, such that (RD(G))ij = 1 dij , if i < j, 0 , if i = j, where dij denotes the distance between the vertices i and j [10, 11]. This matrix (originally known as reciprocal distance matrix [11]) is particulary well-known in chemistry. This is mainly motivated by the importance of the influence of the neighbor atoms when compared with the more distance ones [5, 9, 1]. If we consider a path of order n, with the vertices labeled in the standard way, the Harary matrix, say An = (ai, j), will be defined as ai, j = 1 |i− j| , if i 6= j, 0 , otherwise, (0.1)
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