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

vspace{0.2cm} Suppose G is a simple and connected graph. The first and second Zagreb indices of G are two degree-based graph invariants defined as M1(G)=∑v∈V(G)deg(v)2 and M2(G)=∑e=uv∈E(G)deg(u)deg(v), respectively. The graph G is called p−quasi k−cyclic, 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 all graphs with maximum values of Zagreb indices among all p−quasi k−cyclic graphs with k≤3. & & vspace{0.2cm}