On Banhatti and Zagreb Indices

Abstract

Let G = (V;E) be a connected graph. The Zagreb indices were in-
troduced as early as in 1972. They are dened as M1(G) =
Σ uv2E(G)[dG(u)+ dG(v)] and M2(G) = Σ uv2E(G) dG(u)dG(v), where dG(u) denotes the degree of a vertex u. The K Banhatti indices were introduced by Kulli in  2016. They are dened as B1(G) = Σ ue[dG(u) + dG(e)] and B2(G) = Σ ue dG(u)dG(e),
where ue means that the vertex u and edge e are incident and dG(e) denotes the degree of the edge e in G. These two typ es of indices are closely related. In this paper, we obtain some relations between them. We also provide lower and upper bounds for B1(G) and B2(G) of a connected graph in terms of Zagreb indices.