Name
Abstract | ||
|---|---|---|
We consider a proper coloring c of edges and vertices in a simple graph and the sum f ( v ) of colors of all the edges incident to v and the color of a vertex v . We say that a coloring c distinguishes adjacent vertices by sums, if every two adjacent vertices have different values of f . We conjecture that $${\Delta +\,3}$$ Δ + 3 colors suffice to distinguish adjacent vertices in any simple graph. In this paper we show that this holds for complete graphs, cycles, bipartite graphs, cubic graphs and graphs with maximum degree at most three. |
Year | DOI | Venue |
|---|---|---|
2015 | 10.1007/s00373-013-1399-4 | Graphs and Combinatorics |
Keywords | Field | DocType |
Total proper coloring, Adjacent-vertex-distinguishing index, Neighbor-sum-distinguishing coloring, Total-neighbor-distinguishing index, 05C15 | Discrete mathematics,Edge coloring,Topology,Complete coloring,Combinatorics,Fractional coloring,Chordal graph,Bipartite graph,Neighbourhood (graph theory),Greedy coloring,Mathematics,Graph coloring | Journal |
Volume | Issue | ISSN |
31 | 3 | 1435-5914 |
Citations | PageRank | References |
9 | 0.66 | 6 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Monika Pilsniak | 1 | 29 | 5.42 |
| Mariusz Wozniak | 2 | 111 | 19.51 |