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- Title
On the Chromatic Index of the Signed Generalized Petersen Graph GP (n ,2).
- Authors
Zheng, Shanshan; Cai, Hongyan; Wang, Yuanpei; Sun, Qiang
- Abstract
Let G be a graph and σ : E (G) → { + 1 , − 1 } be a mapping. The pair (G , σ) , denoted by G σ , is called a signed graph. A (proper) l-edge coloring γ of G σ is a mapping from each vertex–edge incidence of G σ to M q such that γ (v , e) = − σ (e) γ (w , e) for each edge e = v w , and no two vertex–edge incidences have the same color; that is, γ (v , e) ≠ γ (v , f) . The chromatic index is the minimal number q such that G σ has a proper q-edge coloring, denoted by χ ′ (G σ) . In 2020, Behr proved that the chromatic index of a signed graph is its maximum degree or maximum plus one. In this paper, we considered the chromatic index of the signed generalized Petersen graph G P (n , 2) and show that its chromatic index is its maximum degree for most cases. In detail, we proved that (1) χ ′ (G P σ (n , 2)) = 3 if n ≡ 3 mod 6 (n ≥ 9) ; (2) χ ′ (G P σ (n , 2)) = 3 if n = 2 p (p ≥ 4) .
- Subjects
PETERSEN graphs; GRAPH coloring; CHARTS, diagrams, etc.
- Publication
Axioms (2075-1680), 2022, Vol 11, Issue 8, pN.PAG
- ISSN
2075-1680
- Publication type
Article
- DOI
10.3390/axioms11080393