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On the Star Chromatic Index of Generalized Petersen Graphs
- Source :
- Discussiones Mathematicae Graph Theory, Vol 41, Iss 2, Pp 427-439 (2021)
- Publication Year :
- 2021
- Publisher :
- University of Zielona Góra, 2021.
-
Abstract
- The star k-edge-coloring of graph G is a proper edge coloring using k colors such that no path or cycle of length four is bichromatic. The minimum number k for which G admits a star k-edge-coloring is called the star chromatic index of G, denoted by χ′s (G). Let GCD(n, k) be the greatest common divisor of n and k. In this paper, we give a necessary and sufficient condition of χ′s (P (n, k)) = 4 for a generalized Petersen graph P (n, k) and show that “almost all” generalized Petersen graphs have a star 5-edge-colorings. Furthermore, for any two integers k and n (≥2k + 1) such that GCD(n, k) ≥ 3, P (n, k) has a star 5-edge-coloring, with the exception of the case that GCD(n, k) = 3, k ≠ GCD(n, k) and n3≡1(mod3){n \over 3} \equiv 1\left( {\bmod 3} \right).
Details
- Language :
- English
- ISSN :
- 20835892
- Volume :
- 41
- Issue :
- 2
- Database :
- Directory of Open Access Journals
- Journal :
- Discussiones Mathematicae Graph Theory
- Publication Type :
- Academic Journal
- Accession number :
- edsdoj.2857b67310094d039ffc56bb387f2b92
- Document Type :
- article
- Full Text :
- https://doi.org/10.7151/dmgt.2195