The first general Zagreb coindex of graph operations

The Hyper-Zagreb Index of Graph Operations

Let G be a simple connected graph. The first and second Zagreb indices have been introduced as  vV(G) (v)2 M1(G) degG and M2(G)  uvE(G)degG(u)degG(v) , respectively, where degG v(degG u) is the degree of vertex v (u) . In this paper, we define a new distance-based named HyperZagreb as e uv E(G) . (v))2 HM(G)     (degG(u)  degG In this paper, the HyperZagreb index of the Cartesian p...

The F-coindex of some graph operations

The F-index of a graph is defined as the sum of cubes of the vertex degrees of the graph. In this paper, we introduce a new invariant which is named as F-coindex. Here, we study basic mathematical properties and the behavior of the newly introduced F-coindex under several graph operations such as union, join, Cartesian product, composition, tensor product, strong product, corona product, disjun...

The first and second Zagreb indices of some graph operations

Reformulated First Zagreb Index of Some Graph Operations

The reformulated Zagreb indices of a graph are obtained from the classical Zagreb indices by replacing vertex degrees with edge degrees, where the degree of an edge is taken as the sum of degrees of the end vertices of the edge minus 2. In this paper, we study the behavior of the reformulated first Zagreb index and apply our results to different chemically interesting molecular graphs and nano-...

On the Multiplicative Zagreb Coindex of Graphs

Abstract. For a (molecular) graph G with vertex set V (G) and edge set E(G), the first and second Zagreb indices of G are defined as M1(G) = ∑ v∈V (G) dG(v) 2 and M2(G) = ∑ uv∈E(G) dG(u)dG(v), respectively, where dG(v) is the degree of vertex v in G. The alternative expression of M1(G) is ∑ uv∈E(G)(dG(u) + dG(v)). Recently Ashrafi, Došlić and Hamzeh introduced two related graphical invariants M...