A Note on the Zeroth-order General Randić Index of Polygonal Cacti

Abstract

The zeroth-order general Randić index of a simple connected graph G is defined as Rα(G) = ∑ u∈V (G) ( d(u) )α , where d(u) is the degree of u and α 6∈ {0, 1} is a real number. A k-polygonal cactus is a connected graph in which every edge lies in exactly one cycle of length k. In this paper, we present the extremal k-polygonal cactus with n cycles for k ≥ 3 with respect to the zeroth-order general Randić index. Mathematics Subject Classification: Primary: 05C15; Secondary: 05C12.