Abstract
For a (molecular) graph, the first Zagreb index M1 is equal to the sum of squares of the degrees of vertices, and the second Zagreb index M2 is equal to the sum of the products of the degrees of pairs of adjacent vertices. Similarly, the hyper Zagreb index is defined as the sum of square of degree of vertices over all the edges. In this paper, First we obtain the hyper Zagreb indices of some derived graphs and the generalized transformations graphs. Finally, the hyper Zagreb indices of double, extended double, thorn graph, subdivision vertex corona of graphs, Splice and link graphs are obtained.
Highlights
All the graphs considered in this paper are connected and simple
A topological index of a graph is a parameter related to the graph
Let G be a connected graph on p vertices and q edges
Summary
All the graphs considered in this paper are connected and simple. For a vertex u ∈ v(G), the degree of the vertex u in G, denoted by dG(u), is the number of edges incident to u in G. Molecular structure descriptors ( called topological indices) are used for modeling physicochemical, pharmacologic, toxicologic, biological and other properties of chemical compounds[2]. Several types of such indices exist, especially those based on vertex and edge distances. One of the most intensively studied topological indices is the wiener index. Let G be a graph on p vertices and q edges. Let G be a connected graph on p vertices and q edges. From the structure of the total graph T (G), it is observe that, for the edge e = uv in T (G), dT (G)(v) = 2dG(v),dT (G)(e) =.
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