Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1709188 | Applied Mathematics Letters | 2012 | 4 Pages |
Abstract
A strong edge coloring of a graph GG is an assignment of colors to the edges of GG such that two distinct edges are colored differently if they are incident to a common edge or share an endpoint. The strong chromatic index of a graph GG, denoted by sχ′(G)sχ′(G), is the minimum number of colors needed for a strong edge coloring of GG. A Halin graph GG is a plane graph constructed from a tree without vertices of degree two by connecting all leaves through a cycle. If a cubic Halin graph GG is different from two particular graphs Ne2Ne2 and Ne4Ne4, then we prove sχ′(G)⩽7sχ′(G)⩽7. This solves a conjecture proposed in W.C. Shiu, W.K. Tam, The strong chromatic index of complete cubic Halin graphs, Appl. Math. Lett. 22 (2009) 754–758.
Related Topics
Physical Sciences and Engineering
Engineering
Computational Mechanics
Authors
Ko-Wei Lih, Daphne Der-Fen Liu,