Abstract
Let [Formula: see text] be a connected graph of order [Formula: see text] and let [Formula: see text] be the reciprocal distance matrix (also called Harary matrix) of the graph [Formula: see text]. Let [Formula: see text] be the eigenvalues of the reciprocal distance matrix [Formula: see text] of the connected graph [Formula: see text] called the reciprocal distance eigenvalues of [Formula: see text]. The Harary energy [Formula: see text] of a connected graph [Formula: see text] is defined as sum of the absolute values of the reciprocal distance eigenvalues of [Formula: see text], that is, [Formula: see text] In this paper, we establish some new lower and upper bounds for [Formula: see text] in terms of different graph parameters associated with the structure of the graph [Formula: see text]. We characterize the extremal graphs attaining these bounds. We also obtain a relation between the Harary energy and the sum of [Formula: see text] largest adjacency eigenvalues of a connected graph.
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