In this note, we obtain the expressions for multiplicative Zagreb indices and coindices of derived graphs such as a line graph, subdivision graph, vertex-semitotal graph, edge-semitotal graph, total graph and paraline graph.

In this paper, we compute the formulae for the third Zagreb indices and its coindices for two classes of graphs such as edge corona product graph, double graph and kth iterated double graph.

Let G be a simple graph with the vertex set V(G) and edge set E(G) respectively. The degree of a vertex v in G is the number of vertices in G which are connected to v by an edge and denoted by dG(v). A topological index is a graph invarient which is numerical parameter obtained from a graph which characterize its topology.Thus for two isomorphic graphG and H the value of a particular topologica...

Measurements of graphs and retrieving structural information complex networks using degree-based network entropy have become an informational theoretical concept. This terminology is extended by the concept Shannon entropy. In this paper, we introduce with having edge weights which are basically redefined Zagreb indices. Some bounds calculated to idealize performance in limiting different kinds...

The second Zagreb index of a graph G is an adjacency-based topological index, which is defined as ∑uv∈E(G)(d(u)d(v)), where uv is an edge of G, d(u) is the degree of vertex u in G. In this paper, we consider the second Zagreb index for bipartite graphs. Firstly, we present a new definition of ordered bipartite graphs, and then give a necessary condition for a bipartite graph to attain the maxim...

Many existing degree based topological indices can be clasified as bond incident degree (BID) indices, whose general form is BID(G) = ∑ uv∈E(G) Ψ(du, dv), where uv is the edge connecting the vertices u, v of the graph G, E(G) is the edge set of G, du is the degree of the vertex u and Ψ is a non-negative real valued (symmetric) function of du and dv. Here, it has been proven that if the extensio...

We consider topological indices I that are sums of f(deg(u))f(deg(v)), where {u, v} are adjacent vertices and f is a function. The Randić connectivity index or the Zagreb group index are examples for indices of this kind. In earlier work on topological indices that are sums of independent random variables, we identified the correlation between I and the edge set of the molecular graph as the ma...