Some New Families of Prime Cordial Graphs

Abstract

In this paper some new families of prime cordial graphs are investigated. We prove that the square graph of path $P_{n}$ is a prime cordial graph for $n=6$ and $n \geq 8$ while the square graph of cycle $C_{n}$ is a prime cordial graph for $n \geq {10}$. We also show that the shadow graph of $K_{1,n}$  for $n \geq 4$ and the shadow graph of $B_{n,n}$ are prime cordial graphs. Moreover we prove that the graphs obtained by mutual duplication of a pair of edges as well as mutual duplication of a pair of vertices from each of two copies of  cycle $C_{n}$ admit prime cordial labeling.