Name
Abstract | ||
|---|---|---|
A strong edge coloring of a graph G is an assignment of colors to the edges of G such that two distinct edges are colored differently if their distance is at most two. The strong chromatic index of graph G, denoted by chi'(s) (G), is the minimum number of colors needed for a strong edge coloring of G. A Halin graph G is a plane graph constructed from a tree T without vertices of degree two by connecting all leaves through a cycle C. In 2018, Hu et al. (2018) posed a conjecture which says that if G = T boolean OR C is a Halin graph other than a wheel W-n, N-e2, or N-e4, then chi'(s) (G) <= chi'(s)(T) + 2. The bound can be achieved. In this paper, we show that the above conjecture is true. This improves the known bound chi'(s) (G) <= chi'(s) (T) + 3 obtained by Lai et al. (2012), and extends the results on Halin graphs G with Delta(G) <= 3 obtained by Lih and Liu (2012) and Delta(G) <= 4 obtained by Hu et al. (2018), respectively. (C) 2021 Elsevier B.V. All rights reserved. |
Year | DOI | Venue |
|---|---|---|
2021 | 10.1016/j.dam.2021.06.016 | DISCRETE APPLIED MATHEMATICS |
Keywords | DocType | Volume |
Strong edge coloring, Strong chromatic index, Halin graph | Journal | 302 |
ISSN | Citations | PageRank |
0166-218X | 0 | 0.34 |
References | Authors | |
0 | 2 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Wei Yang | 1 | 1 | 1.37 |
| Baoyindureng Wu | 2 | 99 | 24.68 |