Maximum Zagreb Indices Among All p-Quasi k-Cyclic Graphs

A simple connected graph G is called a p-quasi k-cyclic graph, if there exists a subset S of vertices such that |S|=p, G-S is k-cyclic and there is no a subset S of V(G) such that |S|<|S| and G-S` is k-cyclic. The aim of this paper is to characterize graph with maximum values of Zagreb indices among all p-quasi k-cyclic graph of order k>=3.