Sum Divisor Cordial Labeling of Wheel Related Graph Families

Abstract

In this paper, we prove that the graphs obtained by switching of a rim in wheel Wn, switching of a vertex of degree 2 and 3 in gear graph Gn, switching of a vertex of degree 2 and 4 in flower graph fln, switching of a vertex of degree 2 and 3 in shell graph Sn are sum divisor cordial (SDC). A sum divisor cordial labeling (SDCL) of a graph G with the vertex set V is a bijection from V to {1, 2, 3, . . . , |V (G) |} such that if each an edge xy is assigned the label 1 if 2 divides [g(x) + g(y)] and 0 otherwise, then the number of edges having label 0 and the number of edges having label 1 under the condition |eg(0)−eg(1)| ≤ 1. If G has a sum divisor cordial labeling (SDCL), then it is called a sum divisor cordial (SDC) graph.