In this paper, the edge a-Zagreb indices and its coindices of some graph operations, such as generalized hierarchical product, Cartesian Product, join, composition of two graphs are obtained. Using the results obtained here, we deduce the F -indices and its coindices for the above graph operation. Finally, we have computed the edge a-Zagreb Index, F -index and their coindices of some important ...

Let G be a simple graph possessing n vertices and m edges. Let di be the degree of the i-th vertex of G , i = 1, . . . , n . The first Zagreb index M1 is the sum of d 2 i over all vertices of G . The second Zagreb index M2 is the sum di dj over pairs of adjacent vertices of G . In this paper we search for graph for which M1/n = M2/m , and show how numerous such graphs can be constructed. In add...

Graph robustness or network is the ability that a graph preserves its connectivity other properties after loss of vertices and edges, which has been central problem in research complex networks. In this paper, we introduce Modified Zagreb index centrality as novel measures to study robustness. We theoretically find some relationships between these measures. Then, use analyze BA scale-free netwo...

Albertson [3] has defined the irregularity of a simple undirected graph G = (V,E) as irr(G) = ∑ uv∈E |dG(u)− dG(v)| , where dG(u) denotes the degree of a vertex u ∈ V . Recently, this graph invariant gained interest in the chemical graph theory, where it occured in some bounds on the first and the second Zagreb index, and was named the third Zagreb index [13]. For general graphs with n vertices...