Chromatic Number of the Corona Product of Complete Graph and Star Graph

Asmarani, Mustika
Yulianti, Kartika
Mulyaning Asih, Endang Cahya

Jurnal Matematika dan Statistika serta Aplikasinya (Jurnal MSA)
Vol 13 No 2 (2025): VOLUME 13 NO 2, 2025

In this paper, we determine the chromatic number of the corona product of complete graph $K_n$ and star graph $K_{1,m}$. Determination of the chromatic numbers is done by observing patterns, constructing conjectures, and proving them formally. We found that the chromatic number of the corona product of complete graph $K_n$ and star graph $K_{1,m}$ is $\chi\left(K_n\odot K_{1,m}\right)=\left\{\begin{matrix}3,\ \ n=1,2\\n,\ n=3,4,\ldots,\ k\\\end{matrix}\right.$, and the chromatic number of the corona product of star graph $K_{1,m}$ and complete graph $K_n$ is $\chi\left(K_{1,m}\odot K_n\right)=n+1,\ n=1,2,\ldots,\ k$. Furthermore, using Matlab software, a program is created to visualize the coloring of the vertices based on the formula that has been obtained.