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All Journal Jurnal Matematika dan Statistika serta Aplikasinya (Jurnal MSA)
Asmarani, Mustika
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Decision Sciences, Operations Research & Management Economics, Econometrics & Finance Environmental Science Mathematics Medicine & Pharmacology

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Chromatic Number of the Corona Product of Complete Graph and Star Graph Asmarani, Mustika; Yulianti, Kartika; Mulyaning Asih, Endang Cahya
Jurnal MSA (Matematika dan Statistika serta Aplikasinya) Vol 13 No 2 (2025): VOLUME 13 NO 2, 2025
Publisher : Universitas Islam Negeri Alauddin Makassar

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.24252/msa.v13i2.56235

Abstract

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.
Co-Authors Kartika Yulianti Mulyaning Asih, Endang Cahya