Some Results On Incidence Energy Of Graphs

The incidence energy of a graph G is de?ned as IE(G) =∑n j=1√μ+j, where μ+j,(j =1, 2, · · ·, n) is the eigenvalue of signless Laplacian matrix of G. In this paper, ?rstly, we consider the incidence energy ordering in trees. The fourth and ?fth smallest incidence energy are characterized by quasi-order method and Coulson integral formula, respectively.The fourth maximal incidence energy among all trees on n vertices is characterized by the relationship of incidence energy and energy. Secondly, given the degree sequence of trees we get the structure of tree with minimum incidence energy. For further analysis, corresponding different degree sequences we ?nd the relationship of minimum incidence energy of trees.Finally, we think about the incidence energy of unicyclic graph, obtain extremal incidence energy with a given girth.