$4$-total mean cordial labeling in subdivision graphs

Document Type: Research Paper


1 Department of Mathematics Sri Parakalyani College Alwarkurichi -627 412, India

2 Sri Paramakalyani College Alwarkurichi-627412, Tamilnadu, India

3 Department of Mathematics Manonmaniam sundarnar university, Abishekapatti, Tirunelveli-627012, Tamilnadu, India


Let $G$ be a graph. Let $f:V\left(G\right)\rightarrow \left\{0,1,2,\ldots,k-1\right\}$ be a function where $k\in \mathbb{N}$ and $k>1$. For each edge $uv$, assign the label $f\left(uv\right)=\left\lceil \frac{f\left(u\right)+f\left(v\right)}{2}\right\rceil$.  $f$ is called $k$-total mean cordial labeling of $G$ if $\left|t_{mf}\left(i\right)-t_{mf}\left(j\right) \right| \leq 1$, for all $i,j\in\left\{0,1,2,\ldots,k-1\right\}$, where $t_{mf}\left(x\right)$ denotes the total number of vertices and edges labelled with $x$, $x\in\left\{0,1,2,\ldots,k-1\right\}$.  A graph with admit a $k$-total mean cordial labeling is called $k$-total mean cordial graph.