Group S_3 Cordial Prime Labeling of Some Graphs

摘要

Let G=(V (G), E(G)) be a graph. Consider the group S3. For u∈S_3, let o(u) denote the order of u in S3. Let G : V (G)→ S_3 be a function defined in such a way that if xy ∈ E(G) (o(g(x)), o(g(y))=1. Let n_j (g) denote the number of vertices of G having label j under g. Now g is called a group S_3 cordial prime labeling if |n_i(g)-n_j (g)| ≤1 for every i, j∈ S_3, i ≠ j. A graph which admits a group S_3 cordial prime labeling is called a group S_3 cordial prime graph. In this paper, we prove that the complete graph, Dumbbell graph, friendship graph and the web graph are group S3 cordial prime.