Geodesic
On the Star Chromatic Index of Generalized Petersen Graphs
Discussiones Mathematicae. Graph Theory, Tome 41 (2021) no. 2, pp. 427-439

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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 n/3≡1(mod3).
Keywords: star edge-coloring, star chromatic index, generalized Petersen graph 
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     title = {On the {Star} {Chromatic} {Index} of {Generalized} {Petersen} {Graphs}},
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Zhu, Enqiang; Shao, Zehui. On the Star Chromatic Index of Generalized Petersen Graphs. Discussiones Mathematicae. Graph Theory, Tome 41 (2021) no. 2, pp. 427-439. http://geodesic.mathdoc.fr/item/DMGT_2021_41_2_a5/