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Neighbor sum distinguishing colorings of graphs with maximum average degree less than $$\tfrac{{37}} {{12}}$$3712
- Source :
- Acta Mathematica Sinica, English Series. 34:265-274
- Publication Year :
- 2017
- Publisher :
- Springer Science and Business Media LLC, 2017.
-
Abstract
- Let G be a graph and let its maximum degree and maximum average degree be denoted by Δ(G) and mad(G), respectively. A neighbor sum distinguishing k-edge colorings of graph G is a proper k-edge coloring of graph G such that, for any edge uv ∈ E(G), the sum of colors assigned on incident edges of u is different from the sum of colors assigned on incident edges of v. The smallest value of k in such a coloring of G is denoted by χ′∑(G). Flandrin et al. proposed the following conjecture that χ′∑ (G) ≤ Δ(G) + 2 for any connected graph with at least 3 vertices and G ≠ C5. In this paper, we prove that the conjecture holds for a normal graph with mad(G) < $$\tfrac{{37}} {{12}}$$ and Δ(G) ≥ 7.
- Subjects :
- Discrete mathematics
Conjecture
Degree (graph theory)
Applied Mathematics
General Mathematics
010102 general mathematics
0102 computer and information sciences
01 natural sciences
Graph
Combinatorics
010201 computation theory & mathematics
Graph power
Bound graph
0101 mathematics
Connectivity
Mathematics
Subjects
Details
- ISSN :
- 14397617 and 14398516
- Volume :
- 34
- Database :
- OpenAIRE
- Journal :
- Acta Mathematica Sinica, English Series
- Accession number :
- edsair.doi...........68ad9aa995be05f1749aa70abb2b502a