Mₑᵛ-Polynomial and Vertex-Edge Topological Indices of Graphs

Abstract

Let  be a simple connected undirected graph with  vertices and  edges, the vertex to edge version of M-polynomial is a graph polynomial based on the comparison between vertices and edges of the graph . We denote the vertex to edge version of M-polynomial by -Polynomial and defined by:  where  are degrees of  vertices  and  are degrees of  edges  which are defined to be the number of neighbors of . In this paper, the  -polynomial and two new proposed vertex-edge version of topological indices, namely vertex-edge versions of geometric arithmetic , and Nirmala  indices have been calculated for selecting graphs.