$k$-Total difference cordial graphs

Abstract

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.