Prime cordial labeling of some wheel related graphs

S. K. Vaidyaa,* and N. H. Shahb

Prime cordial labeling of some wheel related graphs

Authors :

S. K. Vaidya^a,* and N. H. Shah^b

Author Address :

^aDepartment of Mathematics, Saurashtra University, Rajkot - 360005, Gujarat, India.
^bDepartment of Mathematics, Government Polytechnic, Rajkot - 360003, Gujarat, India.

*Corresponding author.

Abstract :

A \textit{prime cordial labeling} of a graph $G$ with the vertex set $V(G)$ is a bijection $f : V(G)\rightarrow \{1,2,3,\ldots,|V(G)|\}$ such that 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 graph which admits prime cordial labeling is called \textit{prime cordial graph}. In this paper we prove that the gear graph $G_{n}$ admits prime cordial labeling for $n \geq 4$. We also show that the helm $H_{n}$ for every $n$, the closed helm $CH_{n}$ (for $n \geq 5$) and the flower graph $Fl_{n}$ (for $n \geq 4$) are prime cordial graphs.