Name
Title | ||
|---|---|---|
On Adjacent Vertex-Distinguishing Total Chromatic Number of Generalized Petersen Graphs |
Abstract | ||
|---|---|---|
Analyzing chromatic number in coloring problem is a tough topic in graph analysis. We focus on the basic theory for a particular type of chromatic number. This will give us insights on the basic topological structure guiding lots of networks in the coming trend of big data era. An adjacent vertex-distinguishing total k-coloring is a proper total k-coloring of a graph G such that for any two adjacent vertices, the set of colors appearing on the vertex and its incident edges are different. The smallest k for which such a coloring of G exists is called the adjacent vertex-distinguishing total chromatic number, and denoted by ?at(G). It has been proved that if the graph G satisfies ?(G)=3, then ?at(G)= 6. However, it is very difficult to determine whether ?at(G)= 5. In this paper, we focus on a special class of 3-regular graphs, the generalized Petersen graphs P(n, k), and show that ?at(P(n, k)) = 5, which improves the bound ?at (P(n, k))= 6. |
Year | DOI | Venue |
|---|---|---|
2016 | 10.1109/DSC.2016.112 | 2016 IEEE First International Conference on Data Science in Cyberspace (DSC) |
Keywords | Field | DocType |
Adjacent Vertex-Distinguishing Total Coloring,Adjacent Vertex-Distinguishing Total Chromatic Number,Generalized Petersen Graph | Complete coloring,Edge coloring,Combinatorics,Graph power,Fractional coloring,Computer science,Botany,Algorithm,Neighbourhood (graph theory),Brooks' theorem,Petersen graph,Adjacent-vertex-distinguishing-total coloring | Conference |
ISBN | Citations | PageRank |
978-1-5090-1193-3 | 0 | 0.34 |
References | Authors | |
5 | 5 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Enqiang Zhu | 1 | 0 | 0.34 |
| Fei Jiang | 2 | 37 | 17.89 |
| Zepeng Li | 3 | 20 | 9.07 |
| Zehui Shao | 4 | 119 | 30.98 |
| Jin Xu | 5 | 230 | 45.13 |