$4$-total mean cordial labeling of union of some graphs with the complete bipartite graph $K_{2,n}$

Let $G$ be a graph. Let $f:Vleft(Gright)rightarrow left{0,1,2,ldots,k-1right}$ be a function where $kin mathbb{N}$ and $k>1$. For each edge $uv$, assign the label $fleft(uvright)=leftlceil frac{fleft(uright)+fleft(vright)}{2}rightrceil$. $f$ is called $k$-total mean cordial labeling of $G$ if $left|t_{mf}left(iright)-t_{mf}left(jright) right| leq 1$, for all $i,jinleft{0,1,2,ldots,k-1right}$, where $t_{mf}left(xright)$ denotes the total number of vertices and edges labelled with $x$, $xinleft{0,1,2,ldots,k-1right}$. A graph with admit a $k$-total mean cordial labeling is called $k$-total mean cordial graph. In this paper, we investigate the $4$-total mean cordial labeling of some graphs derived from the complete bipartite graph $K_{2,n}$.