Computing the First and Third Zagreb Polynomials of Cartesian Product of Graphs

Document Type : Research Paper


1 Islamic Azad University, Arak Branch, I. R. Iran

2 University of Kashan, I. R. Iran


Let G be a graph. The first Zagreb polynomial M1(G, x) and the third Zagreb polynomial M3(G, x) of the graph G are defined as:     ( ) ( , ) [ ] e uv E G G x x d(u) + d(v) M1 , ( , )  euvE(G) G x x|d(u) - d(v)| M3 . In this paper, we compute the first and third Zagreb polynomials of Cartesian product of two graphs and a type of dendrimers.