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.
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This research is supported by the National Natural Science Foundation of China(10471037)and the Education Committee of Hunan Province(02C210)(04B047).
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Wang, H., Deng, H. Unicycle Graphs with Maximum Generalized Topological Indices. J Math Chem 42, 119–124 (2007). https://doi.org/10.1007/s10910-005-9027-z
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DOI: https://doi.org/10.1007/s10910-005-9027-z