Strong edge chromatic index of the generalized Petersen graphs

Yang, Zixuan; Wu, Baoyindureng

doi:10.1016/j.amc.2017.10.047

Cited by 5 publications

(2 citation statements)

References 23 publications

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“…They got specific values for GP(n, 1) with n ≥ 3, and for GP(n, 2) with 4 ≤ n ≤ 7. Yang et al [17] studied the strong chromatic index of GP(n, k) when 1 ≤ k ≤ 3. In [18], Cai et al studied the edge coloring of the generalized Petersen graph and got the following results.…”

Section: Introductionmentioning

confidence: 99%

On the Chromatic Index of the Signed Generalized Petersen Graph GP(n,2)

Zheng

Cai

Wang

et al. 2022

Axioms

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Let G be a graph and σ:E(G)→{+1,−1} be a mapping. The pair (G,σ), denoted by Gσ, is called a signed graph. A (proper) l-edge coloring γ of Gσ is a mapping from each vertex–edge incidence of Gσ to Mq such that γ(v,e)=−σ(e)γ(w,e) for each edge e=vw, 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 Gσ has a proper q-edge coloring, denoted by χ′(Gσ). 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 GP(n,2) and show that its chromatic index is its maximum degree for most cases. In detail, we proved that (1) χ′(GPσ(n,2))=3 if n≡3 mod 6(n≥9); (2) χ′(GPσ(n,2))=3 if n=2p(p≥4).

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Section: Introductionmentioning

confidence: 99%

On the Chromatic Index of the Signed Generalized Petersen Graph GP(n,2)

Zheng

Cai

Wang

et al. 2022

Axioms

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show abstract

“…Figure 1 is an illustration of generalized Petersen graph P(n, k) with n = 9 and k = 4. In 2018, Wu and Yang [15] conjectured that every generalized Petersen graph P(n, k) with n > 2k and k ≥ 4 can be strong edge colored with 7 colors. In the same paper, they showed some upper bound of strong chromatic index of P(n, k) with k ∈ {1, 2, 3}.…”

Section: Introductionmentioning

confidence: 99%

Strong Edge Coloring of Generalized Petersen Graphs

2020

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A strong edge coloring of a graph G is a proper edge coloring such that every color class is an induced matching. In 2018, Yang and Wu proposed a conjecture that every generalized Petersen graph P(n,k) with k≥4 and n>2k can be strong edge colored with (at most) seven colors. Although the generalized Petersen graph P(n,k) is a kind of special graph, the strong chromatic index of P(n,k) is still unknown. In this paper, we support the conjecture by showing that the strong chromatic index of every generalized Petersen graph P(n,k) with k≥4 and n>2k is at most 9.

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Determining the edge metric dimension of the generalized Petersen graph P(n, 3)

Wang

Zhang

2021

J Comb Optim

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Strong edge chromatic index of the generalized Petersen graphs

Cited by 5 publications

References 23 publications

On the Chromatic Index of the Signed Generalized Petersen Graph GP(n,2)

On the Chromatic Index of the Signed Generalized Petersen Graph GP(n,2)

Strong Edge Coloring of Generalized Petersen Graphs

Determining the edge metric dimension of the generalized Petersen graph P(n, 3)

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