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All Journal Mathematics and Applications (MAp) Journal
Yeni Rahma Oktaviani
"Lambung Mangkurat University"
Mathematics

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EDGE COLORING CYCLE BOOKS GRAPH B_(C_n,m) Yeni Rahma Oktaviani; Saman Abdurrahman
MAp (Mathematics and Applications) Journal Vol 8, No 1 (2026)
Publisher : Universitas Islam Negeri Imam Bonjol Padang

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.15548/map.v8i1.13832

Abstract

This study investigates the edge coloring of the cycle book graphs, denoted as B_(C_n,m), which consist of m cycles C_n intersection at a shared P_2 path. The primary objective is to identify the chromatic index-the fewest colors needed to ensure no two adjacent edges share the same color. Utilizing a deductive approach, the researchers developed an edge coloring function based on cyclic patterns for both even and odd values of n. The findings establish that the chromatic index χ' (B_(C_n,m) )= m+1 for all n≥3 and m≥2. This result is validated by coloring construction that aligns with the lower bound established by Vizing’s Theorem
Co-Authors Saman Abdurrahman