# Incident Vertex \(\pi\)-Coloring of Graphs

## DOI:

https://doi.org/10.26713/cma.v14i2.2215## Keywords:

π coloring of graphs, Incident vertex π coloring, Fan graphs, Friendship graphs, Wheel graphs, Diamond graphs, Star and Double Star graphs## Abstract

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.

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*Communications in Mathematics and Applications*,

*14*(2), 591–604. https://doi.org/10.26713/cma.v14i2.2215

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