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Per-Spectral Characterizations Of Some Bipartite Graphs

Tingzeng Wu;  Heping Zhang — 2017

Discussiones Mathematicae Graph Theory

A graph is said to be characterized by its permanental spectrum if there is no other non-isomorphic graph with the same permanental spectrum. In this paper, we investigate when a complete bipartite graph Kp,p with some edges deleted is determined by its permanental spectrum. We first prove that a graph obtained from Kp,p by deleting all edges of a star K1,l, provided l < p, is determined by its permanental spectrum. Furthermore, we show that all graphs with a perfect matching obtained from Kp,p...

Extremal Matching Energy of Complements of Trees

Tingzeng Wu;  Weigen Yan;  Heping Zhang — 2016

Discussiones Mathematicae Graph Theory

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...

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