Gutman and Wagner proposed the concept of the matching energy which is defined as the sum of the absolute values of the zeros of the matching polynomial of a graph. And they pointed out that the chemical applications of matching energy go back to the 1970s. Let T be a tree with n vertices. In this paper, we characterize the trees whose complements have the maximal, second-maximal and minimal matching energy. Furthermore, we determine the trees with edge-independence number p whose complements have the minimum matching energy for p = 1, 2, . . . , [n/2]. When we restrict our consideration to all trees with a perfect matching, we determine the trees whose complements have the second-maximal matching energy.
@article{bwmeta1.element.doi-10_7151_dmgt_1869,
author = {Tingzeng Wu and Weigen Yan and Heping Zhang},
title = {Extremal Matching Energy of Complements of Trees},
journal = {Discussiones Mathematicae Graph Theory},
volume = {36},
year = {2016},
pages = {505-521},
zbl = {1339.05329},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_7151_dmgt_1869}
}
Tingzeng Wu; Weigen Yan; Heping Zhang. Extremal Matching Energy of Complements of Trees. Discussiones Mathematicae Graph Theory, Tome 36 (2016) pp. 505-521. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_7151_dmgt_1869/
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