Name
Abstract | ||
|---|---|---|
Two vertices u and v in a nontrivial connected graph G are twins if u and v have the same neighbors in V (G) - {u, v}. If u and v are adjacent, they are referred to as true twins; while if u and v are nonadjacent, they are false twins. For a positive integer k, let c : V (G) -> Z(k) be a vertex coloring where adjacent vertices may be assigned the same color. The coloring c induces another vertex coloring c' : V (G) -> Z(k) defined by c'(v) = Sigma(c(u))(u is an element of N[v]) for each v is an element of V (G), where N [v] is the closed neighborhood of v. Then c is called a closed modular k-coloring if c'(u) not equal = c'(v) in Z(k) for all pairs u, v of adjacent vertices that are not true twins. The minimum k for which G has a closed modular k - coloring is the closed modular chromatic number (mc) over bar (G) of G. The closed modular chromatic number is investigated for trees and determined for several classes of trees. For each tree T in these classes, it is shown that (mc) over bar (T) = 2 or (mc) over bar (T) = 3. A closed modular k - coloring c of a tree T is called nowhere - zero if c (x) not equal 0 for each vertex x of T. It is shown that every tree of order 3 or more has a nowhere - zero closed modular 4-coloring. |
Year | DOI | Venue |
|---|---|---|
2013 | 10.7151/dmgt.1678 | DISCUSSIONES MATHEMATICAE GRAPH THEORY |
Keywords | Field | DocType |
trees,closed modular k-coloring,closed modular chromatic number | Discrete mathematics,Combinatorics,Modular design,Mathematics | Journal |
Volume | Issue | ISSN |
33 | 2 | 1234-3099 |
Citations | PageRank | References |
0 | 0.34 | 1 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Bryan Phinezy | 1 | 0 | 0.34 |
| Ping Zhang | 2 | 292 | 47.70 |