Name
Abstract | ||
|---|---|---|
For a nontrivial connected graph G, let $${c: V(G)\to {{\mathbb N}}}$$be a vertex coloring of G, where adjacent vertices may be colored the same. For a vertex v of G, let N(v) denote the set of vertices adjacent to v. The color sum σ(v) of v is the sum of the colors of the vertices in N(v). If σ(u) ≠ σ(v) for every two adjacent vertices u and v of G, then c is called a sigma coloring of G. The minimum number of colors required in a sigma coloring of a graph G is called its sigma chromatic number σ(G). The sigma chromatic number of a graph G never exceeds its chromatic number χ(G) and for every pair a, b of positive integers with a ≤ b, there exists a connected graph G with σ(G) = a and χ(G) = b. There is a connected graph G of order n with σ(G) = k for every pair k, n of positive integers with k ≤n if and only if k ≠ n − 1. Several other results concerning sigma chromatic numbers are presented. |
Year | DOI | Venue |
|---|---|---|
2009 | 10.1007/s00373-010-0952-7 | Graphs and Combinatorics |
Keywords | DocType | Volume |
order n,sigma coloring,positive integer,chromatic number,adjacent vertices u,sigma chromatic number,nontrivial connected graph,connected graph,graph g,minimum number,neighbor-distinguishing coloring · sigma coloring | Journal | 26 |
Issue | ISSN | Citations |
6 | 0911-0119 | 2 |
PageRank | References | Authors |
0.78 | 3 | 4 |
Name | Order | Citations | PageRank |
|---|---|---|---|
| gary chartrand | 1 | 2 | 0.78 |
| Futaba Okamoto | 2 | 43 | 5.09 |
| Ping Zhang | 3 | 292 | 47.70 |
| Ping Zhang | 4 | 292 | 47.70 |