%0 Journal Article %T $4$-total mean cordial labeling of special graphs %J Journal of Algorithms and Computation %I University of Tehran %Z 2476-2776 %A Ponraj, R %A SUBBULAKSHMI, S %A Somasundaram, S %D 2021 %\ 06/01/2021 %V 53 %N 1 %P 13-22 %! $4$-total mean cordial labeling of special graphs %R 10.22059/jac.2021.81169 %X 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 $i,j\in\left\{0, 1, \ldots, k-1\right\}$, 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. %U https://jac.ut.ac.ir/article_81169_28389b60f46526921271f4681f287da6.pdf