Cordiality in the path union of vertex switching of wheel graphs in increasing order

Abstract

The cordial labeling of a graph $G$ is a function $f:V\left(G\right)\to \left\{0,1\right\}$ such that every edge $uv$ in $G$ is consigned the label $\left|f\left(u\right)-f\left(v\right)\right|$ with the property $\left|v_{f} \left(0\right)-v_{f} \left(1\right)\right|\le 1$ and $\left|e_{f*} \left(0\right)-e_{f*} \left(1\right)\right|\le 1$, where the number of vertices is denoted by $v_{f} \left(i\right)$ for $i = 0,1 $ and the number of edges is denoted as $e_{f*} \left(i\right)$ for $i = 0,1$.  The graph which concedes cordial labeling is called a cordial graph.  In this paper, we prove that the path union of vertex switching of wheel graphs is cordial.