Subtract Divisor Cordial Labeling of Ring Sum of a Graphs

Abstract

Abstract: A subtract divisor cordial labeling of a graph G with vertex set is a bijection f from V to {1, 2,…, |V|} such that an edge is assigned the label 1 if 2 divides (f(u) – f(v)) and 0 otherwise, then number of edges labeled with 0 and the number of edges labeled with 1 differ by at most 1. A graph with a subtract divisor cordial labeling is called a subtract divisor cordial graph. In this paper, I have Proved that ring sum of cycle with star graph, cycle with one chord with star graph, cycle with twin chords with star graph and cycle with triangle with star graphs are subtract divisor cordial graph. I also proved that ring sum of wheel with star graph, flower graph with star graph, gear graph with star graph and path graph with star graph are subtract divisor cordial graphs. Further I proved that shell graph with star graph are subtract divisor cordial graphs. And in last I proved that double fan with star graphs are subtract divisor cordial graph.

AMS Subject classification number: 05C78

Keywords: Subtract divisor cordial labeling, ring sum, shell graph, double fan, gear graph

Cite this Article: A. H. Rokad. Subtract Divisor Cordial Labeling of Ring Sum of a Graphs. Research & Reviews: Discrete Mathematical Structures. 2019; 6(3): 23–28p.