Abstract
Abstract The Harary index is defined as the sum of reciprocals of distances between all pairs of vertices of a connected graph. In this paper, expressions for the Harary indices of the join, corona product, Cartesian product, composition and disjunction of graphs are derived and the indices for some well-known graphs are evaluated. In derivations some terms appear which are similar to the Harary index and we name them the second and third Harary index. MSC:05C05, 05C07, 05C90.
Highlights
Introduction and preliminariesThroughout this paper we consider simple connected graphs without loops and multiple edges
Suppose that G is a graph with vertex set V (G) = {v, v, . . . , vn} and edge set E(G)
We propose two more members of the class of Harary indices, the second Harary index and the third Harary index, which are as follows:
Summary
Introduction and preliminariesThroughout this paper we consider simple connected graphs without loops and multiple edges. In Section , we obtain lower and upper bounds on the Harary index of graphs. Corollary Let G ( K|G|) be a connected graph of order |G|, G edges and diameter D(G).
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