$k$-Total prime cordial labeling of graphs

Document Type: Research Paper

Authors

1 Department of Mathematics, Sri Paramakalyani College, Alwarkurichi-627412

2 Research Scholar, Department of Mathematics Manonmaniam sundarnar university, Abishekapatti, Tirunelveli-627 012, Tamilnadu, India.

3 Department of Mathematics, Manonmaniam sundarnar university, Abishekapatti, Tirunelveli-627 012, Tamilnadu, India.

Abstract

In this paper we introduce a new graph labeling method called $k$-Total prime cordial. Let $G$ be a $(p,q)$ graph. Let $f:V(G)\to\{1,2, \ldots, k\}$ be a map where $k \in \mathbb{N}$ and $k>1$. For each edge $uv$, assign the label $gcd(f(u),f(v))$. $f$ is called $k$-Total prime cordial labeling of $G$ if $\left|t_{f}(i)-t_{f}(j)\right|\leq 1$, $i,j \in \{1,2, \ldots, k\}$ where $t_{f}(x)$ denotes the total number of vertices and the edges labeled with $x$. We investigate k-total prime cordial labeling of some graphs and study the 4-total prime cordial labeling of path, cycle, complete graph etc.

Keywords