Extremal matching energy of complements of trees

Abstract

The matching energy is defined as the sum of the absolute values of the zeros of the matching polynomial of a graph, which is proposed first by Gutman and Wagner [The matching energy of a graph, Discrete Appl. Math. 160 (2012) 2177-2187]. And they gave some properties and asymptotic results of the matching energy. In this paper, we characterize the trees with n vertices whose complements have the maximal, second-maximal and minimal matching energy.Further, we determine the trees with a perfect matching whose complements have the secondmaximal matching energy. In particular, show that the trees with edge-independence number number p whose complements have the minimum matching energy for p = 1, 2, . . . , ⌊ n 2 ⌋.

Extremal Matching Energy of Random Polyomino Chains

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Two Classes of Topological Indices of Phenylene Molecule Graphs

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Hosoya Index ofL-Type Polyphenyl Spiders

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