Note: Sharp bounds of the zeroth-order general Randić index of bicyclic graphs with given pendent vertices

Authors:
Xiang-Feng Pan;Ning-Ning Lv
Affiliations:
School of Mathematical Sciences, Anhui University, Hefei, Anhui, 230601, PR China;Department of Public Courses, Anhui Xinhua University, Hefei, Anhui, 230088, PR China and School of Mathematical Sciences, Anhui University, Hefei, Anhui, 230601, PR China
Venue:
Discrete Applied Mathematics
Year:
2011

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Abstract

Let G be a simple connected graph and @a be a given real number. The zeroth-order general Randic index of ^0R"@a(G) is defined as @?"v"@?"V"("G")[d"G(v)]^@a, where d"G(v) denotes the degree of the vertex v of G. In this paper, for any @a(0,1), we give sharp bounds of the zeroth-order general Randic index ^0R"@a of all bicyclic graphs with n vertices and k pendent vertices.