Difference Cordial Labeling in context of Joint sum of Graphs

Abstract

Suppose G be a (p, q) graph. Suppose f  be a map from f(G) to {1,2,...,p}. For each edge xy assign, the label |f(x) – f(y)|. f is difference cordial if  f is 1-1 and |e_f(0) – e_f(1)| 14≤">  1, where e_f(1) and e_f(0) denote the number of edges with labeled 1 except labeled with 1 respectively. A graph which admit difference cordial labeling is called a difference cordial graph.

            In this paper I prove the following results.

1. The joint sum of two copies of wheel graph is difference cordial.
2. The joint sum of two copies of shell graph is difference cordial.
3. The joint sum of two copies of double wheel graph is difference cordial.
4. The joint sum of two copies of Petersen graph is difference cordial.
5. The joint sum of two copies of coconut tree is difference cordial.