New Construction on SD-Prime Cordial Labeling

Abstract

Given a bijection $f:V(G) \rightarrow \{1,2,\cdots ,|V(G)|\}$, we associate two integers $S=f(u)+f(v)$ and $D=|f(u)-f(v)|$ with every edge uv in E(G). The labeling f induces an edge labeling $f':E(G) \rightarrow \{0,1\}$ such that for any edge uv in E(G), $f'(uv)=1$ if $gcd(S,D)=1$, and $f'(uv)=0$ otherwise. Let $e_{f'}(i)$ be the number of edges labeled with $i \in \{0,1\}$. We say f is SD-prime cordial labeling if $|e_{f'}(0)-e_{f'}(1)| \le 1$. Moreover G is SD-prime cordial if it admits SD-prime cordial labeling. In this paper, we investigate some new construction of SD-prime cordial graph.