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- Title
Neighbor sum distinguishing edge coloring of subcubic graphs.
- Authors
Yu, Xiao; Wang, Guang; Wu, Jian; Yan, Gui
- Abstract
A proper edge- k-coloring of a graph G is a mapping from E( G) to {1, 2,..., k} such that no two adjacent edges receive the same color. A proper edge- k-coloring of G is called neighbor sum distinguishing if for each edge uv ∈ E( G), the sum of colors taken on the edges incident to u is different fromthe sumof colors taken on the edges incident to v. Let χ′( G) denote the smallest value k in such a coloring of G. This parameter makes sense for graphs containing no isolated edges (we call such graphs normal). The maximum average degree mad( G) of G is the maximum of the average degrees of its non-empty subgraphs. In this paper, we prove that if G is a normal subcubic graph with mad( G) < 5/2, then χ′( G) ≤ 5. We also prove that if G is a normal subcubic graph with at least two 2-vertices, 6 colors are enough for a neighbor sum distinguishing edge coloring of G, which holds for the list version as well.
- Subjects
SUBGRAPHS; PLANAR graphs; GEOMETRIC vertices; ISOMORPHISM (Mathematics); BIPARTITE graphs
- Publication
Acta Mathematica Sinica, 2017, Vol 33, Issue 2, p252
- ISSN
1439-8516
- Publication type
Article
- DOI
10.1007/s10114-017-5516-9