$k$-Total difference cordial graphs

Document Type: Research Paper


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

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

3 Manonmaniam Sundaranar University, Tirunelveli-627012, Tamilnadu, India.


Let $G$ be a graph. Let $f:V(G)\to\{0,1,2, \ldots, k-1\}$ be a map where $k \in \mathbb{N}$ and $k>1$. For each edge $uv$, assign the label $\left|f(u)-f(v)\right|$. $f$ is called a $k$-total difference cordial labeling of $G$ if $\left|t_{df}(i)-t_{df}(j)\right|\leq 1$, $i,j \in \{0,1,2, \ldots, k-1\}$ where $t_{df}(x)$ denotes the total number of vertices and the edges labeled with $x$.A graph with admits a $k$-total difference cordial labeling is called a $k$-total difference cordial graphs. We investigate $k$-total difference cordial labeling of some graphs and study the $3$-total difference cordial labeling behaviour of star,bistar,complete bipartiate graph,comb,wheel,helm,armed crown etc.