Reduced Second Zagreb Index of Unicyclic Graphs

Abstract

Recently a novel degree based topological index, reduced second Zagreb index, defined for any connected graph as follows: RM2 = Sigma(uv is an element of E(G)) (d(u) - 1)(d(v) - 1) where d(u) and d(v) are the number of edges incident to the vertices u and v, respectively. We determine the minimum and maximum reduced second Zagreb index in the class of n-vertex unicyclic graphs and characterize the corresponding extremal graphs.