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Unicycle Graphs with Maximum Generalized Topological Indices

Authors:	Hongzhuan Wang Hanyuan Deng

Institution:	(1) Department of Mathematics, Hunan Normal University, Changsha, Hunan, 410081, P. R. China

Abstract:	Let G be an unicycle graph and d _v the degree of the vertex v. In this paper, we investigate the following topological indices for an unicycle graph $G: \alpha_m (G)=\sum_{v \in V(G)}{d_v}^m, \alpha_{-m}(G)=\sum_{v\in V(G)}{d_v}^{-m}$ , $\alpha_{-\frac{1}{m}}(G)=\sum_{v\in V(G)}{d_v}^{-\frac{1}{m}}$ , where m ≥ 2 is an integer. All unicycle graphs with the largest values of the three topological indices are characterized. This research is supported by the National Natural Science Foundation of China(10471037)and the Education Committee of Hunan Province(02C210)(04B047).

Keywords:	Unicyclic graph the generalied topological index the Zeroth-order Randic index
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