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On Unicycle Graphs with Maximum and Minimum Zeroth-order Genenal Randić Index |
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| Authors: | Hongbo Hua Hanyuan Deng |
| Institution: | (1) Department of Computer science, Huaiyin Institute of Technology, Huaian, Jiangsu, 223001, P.R. China;(2) College of Mathematics and Computer science, Hunan Normal University, Changsha, Hunan, 410081, P.R. China |
| Abstract: | Let G be a graph and d v denote the degree of the vertex v in G. The zeroth-order general Randić index of a graph is defined as R α0(G) = ∑ v∈V(G) d v α where α is an arbitrary real number. In this paper, we obtained the lower and upper bounds for the zeroth-order general Randić index R α0(G) among all unicycle graphs G of order n. We give a clear picture for R α0(G) of unicycle graphs according to real number α in different intervals. |
| Keywords: | unicycle graph zeroth-order general Randić index minimum cardinality maximum cardinality |
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