Abstract
A PCL of G is a bijective map g from V to {1, 2, 3, |V|} in such a way that if an edge st is given label 1 if GCD(g(s), g(t)) = 1 & 0 otherwise, then the edges given 0 & 1 differ by at most 1 i.e; |eg (0) − eg (1)| ≤ 1. If a graph permits a PCL, then it is called a PCG. In this paper, we prove that lilly graph admits a PCL. Further, we have shown that lilly graph under some graph operations like switching of a vertex, duplication of a vertex, degree splitting graph and barycentric subdivision admits a PCL which may find its application in the development of artificial intelligence.
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