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All Journal BAREKENG: Jurnal Ilmu Matematika dan Terapan Compiler
Jaya Santoso
IT DEL
Computer Science & IT Control & Systems Engineering Economics, Econometrics & Finance Energy Engineering Mathematics Mechanical Engineering Physics Transportation

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Journal : Compiler

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On the Chromatic Number of Cycle Books Graph Santoso, Jaya
Compiler Vol 14, No 1 (2025): May
Publisher : Institut Teknologi Dirgantara Adisutjipto

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.28989/compiler.v14i1.2930

Abstract

Graph coloring is a fundamental topic in graph theory, with various applications in scheduling, networking, and optimization problems. In this study, we investigate the chromatic number of the cycle books graph , a structured graph formed by attaching multiple cycles to a common path . We establish that the chromatic number of    depends on the parity of . Specifically, we prove that if  is even, the chromatic number is , while if  is odd, the chromatic number is . These results provide a deeper understanding of coloring properties in book-like graphs and contribute to the broader study of chromatic numbers in structured graph families. The findings may be extended to other variations of book graphs and related topologies in future research.
Co-Authors Darmaji Darmaji