Study of some connectivity index of subdivided mk graphs of ladder and triangular ladder graph

Abstract

An m^k-graph of a graph G is defined by taking m ≥ 2 copies G₁, … , G_m of a graph G in which every vertex u_h of copy G_h is adjacent to a corresponding vertex v_m of copy G_m. An m^k-graph is represented by m^k(G). In this paper we work on some degree based connectivity indices of subdivided m^k-graph generated by ladder and triangular ladder graph. Also closed formulas for computing various degree based topological indices of said families of graphs have been presented.

Subject Classification:

• Primary 93A30
• Secondary 49K15

Keywords:

• m^k-graph
• Ladder graph
• Triangular ladder graph
• Zagreb indices
• Augmented Zagreb index