Name
Title | ||
|---|---|---|
A characterization for the neighbor-distinguishing total chromatic number of planar graphs with Δ=13. |
Abstract | ||
|---|---|---|
The neighbor-distinguishing total chromatic number χa′′(G) of a graph G is the smallest integer k such that G can be totally colored using k colors with a condition that any two adjacent vertices have different sets of colors. In this paper, we give a sufficient and necessary condition for a planar graph G with maximum degree 13 to have χa′′(G)=14 or χa′′(G)=15. Precisely, we show that if G is a planar graph of maximum degree 13, then 14≤χa′′(G)≤15; and χa′′(G)=15 if and only if G contains two adjacent 13-vertices. |
Year | DOI | Venue |
|---|---|---|
2018 | 10.1016/j.disc.2018.07.011 | Discrete Mathematics |
Keywords | Field | DocType |
Planar graph,Neighbor-distinguishing total coloring,Discharging,Combinatorial Nullstellensatz | Integer,Discrete mathematics,Graph,Combinatorics,Colored,Chromatic scale,Vertex (geometry),Degree (graph theory),Mathematics,Planar graph | Journal |
Volume | Issue | ISSN |
341 | 11 | 0012-365X |
Citations | PageRank | References |
0 | 0.34 | 7 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Jingjing Huo | 1 | 7 | 3.06 |
| Weifan Wang | 2 | 868 | 89.92 |
| Yiqiao Wang | 3 | 494 | 42.81 |