ON VERTEX-EDGE ECCENTRIC CONNECTIVITY INDEX AND CORONA PRODUCT OF GRAPHS

Abstract

In agraph G=(V,E), a vertex v∈V, ve-dominates every edge incident to it as well as every edge adjacent to these incident edges. The vertex-edge degree of a vertex v, is denoted by d_ve (v) and is the number of edges v e-dominated by v. In this paper, we introduce the vertex-edge eccentric connectivity index of a graph G, denoted by 〖ξ^C〗_vee (G) and is equal to the sum of the product of the connectivity and ve-degree of the vertices of G. We calculate the vertex-edge eccentricity connectivity index of if certain graphs. More specifically, we obtain the vertex-edge eccentricity connectivity index of the corona product of K_2 withC_n,C_(1,n-1),K_n, K_(m,n). Finally, we obtain some upper and lower bounds on 〖ξ^C〗_vee (G).