Bounds of F-index for unicyclic graphs with fixed pendent vertices

Abstract

Furtula and Gutman [J. Math. Chem., 53 (4) (2015), 1184- 1190] reinvestigated the FF-index as a sum of cubes of the degrees of all the vertices in a chemical graph and proved its various properties. A connected graph with equal order and size is called unicyclic graph, where order is number of vertices and size is number of edges. In this paper, we characterize the extremal graphs in a family of graphs called by unicyclic graphs with fixed number of pendent vertices. We also investigate the bound on FF-index in the same family of graphs i.e 4(2n+3α)≤F(G)≤8n+α(α+2)(α+3)4(2n+3α)≤F(G)≤8n+α(α+2)(α+3) for each G∈UαnG∈Unα, where UαnUnα is a class of all the unicyclic graphs such that the order of each graph is nn with αα pendent vertices.