Incident Vertex \(\pi\)-Coloring of Graphs
Sunil Thakare, Haribhau R. Bhapkar · Communications in Mathematics and Applications · 2023
We defined the concept of \(\pi\)-coloring of graphs and incident vertex \(\pi\) coloring of graphs. The incident vertex \(\pi\) coloring number \((IV \pi CN)\) of graphs is different from all existing coloring techniques. The \(IV \pi CN\) of complete graph \((K_n)\) is \(n\). \(IV \pi CN\) of wheel, star, double star graph are \((n+1)\). Also, \(IV \pi CN\) of friendship, diamond and fan graphs are \(\Delta+1\). The \(IV \pi CN\) of double fan graph is \(\Delta+2\). The \(IV \pi CN\) of complete bipartite graphs \(K_{m,n}\) is \((m+n)\). The \(IV \pi CN\) of bipartite graph is bounded. Moreover, some results associated to enumeration of the number of graphs having equal incident vertex \(\pi\) chromatic number of few families are proved.