EDGE COLORING CYCLE BOOKS GRAPH B_(C_n,m)

Yeni Rahma Oktaviani ("Lambung Mangkurat University")
Saman Abdurrahman (Lambung Mangkurat University)

Mathematics and Applications (MAp) Journal
Vol 8, No 1 (2026)

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