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