Difference Cordial Labeling of the Graphs Related to Duplication of an Edge or Vertex of a Cycle and Total Graph

Abstract. A difference cordial labeling of a graph G is a bijective function f from V(G) onto {1, 2, 3, ⋯ , |V(G)|} such that each edge uv is assigned the label 1 if |f(u) – f(v)| = 1, and the label 0 otherwise, satisfying the condition that the number of edges labeled with 1 and the number of edges labeled with 0 differ by at most 1. A graph with difference cordial labeling is called a difference cordial graph. In this paper we proved that the umbrella graph U(m, n), duplication of a vertex by an edge in a cycle Cn, duplication of an edge by a vertex in a cycle Cn and the total graph of a path Pn are difference cordial graphs.