On Prime Cordial Labelings of Double Triangular Snake
Xi Yue, Wing-Ning Li · 2016
A prime cordial labeling of a graph G with vertex set V is a bijection f from V to {1, 2, ..., |V|} such that if each edge uv is assigned the label 1 if gcd(f(u), f(v)) = 1 and 0 if gcd(f(u), f(v))> 1, then the number of edges labeled with 0 and the number of edges labeled with 1 differ by at most 1. A double triangular snake is a graph formed by two triangular snakes having a common path, i.e., a double triangular snake with p blocks is obtained from a path ν1, ν2, ..., νp+ 1 by joining νiand νi+1to two new vertices νp+1+iand ν2p+1+ifor i = 1, 2, ..., p. In this paper, we show that double triangular snakes are prime cordial for all p ≥ 3.