English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Tools annual

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

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).

On the star chromatic index of generalized Petersen graphs