PL EN

Preferencje
Język
Widoczny [Schowaj] Abstrakt
Liczba wyników
Czasopismo

## Discussiones Mathematicae Graph Theory

2012 | 32 | 1 | 81-90
Tytuł artykułu

### Recognizable colorings of cycles and trees

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
For a graph G and a vertex-coloring c:V(G) → {1,2, ...,k}, the color code of a vertex v is the (k+1)-tuple (a₀,a₁, ...,aₖ), where a₀ = c(v), and for 1 ≤ i ≤ k, $a_i$ is the number of neighbors of v colored i. A recognizable coloring is a coloring such that distinct vertices have distinct color codes. The recognition number of a graph is the minimum k for which G has a recognizable k-coloring. In this paper we prove three conjectures of Chartrand et al. in [8] regarding the recognition number of cycles and trees.
Słowa kluczowe
EN
Kategorie tematyczne
Wydawca
Czasopismo
Rocznik
Tom
Numer
Strony
81-90
Opis fizyczny
Daty
wydano
2012
otrzymano
2010-07-16
poprawiono
2011-01-25
zaakceptowano
2011-01-25
Twórcy
autor
• Department of Mathematics, University of Johannesburg, Johannesburg, South Africa
autor
• Department of Mathematics and Applied Mathematics, University of the Free State, Bloemfontein, South Africa
Bibliografia
• [1] M. Aigner and E. Triesch, Irregular assignments and two problems á la Ringel, in: Topics in Combinatorics and Graph Theory, R. Bodendiek and R. Henn, eds. (Physica, Heidelberg, 1990) 29-36.
• [2] M. Aigner, E. Triesch and Z. Tuza, Irregular assignments and vertex-distinguishing edge-colorings of graphs, Combinatorics' 90 (Elsevier Science Pub., New York, 1992) 1-9.
• [3] A.C. Burris, On graphs with irregular coloring number 2, Congr. Numer. 100 (1994) 129-140.
• [4] A.C. Burris, The irregular coloring number of a tree, Discrete Math. 141 (1995) 279-283, doi: 10.1016/0012-365X(93)E0225-S.
• [5] G. Chartrand, H. Escuadro, F. Okamoto and P. Zhang, Detectable colorings of graphs, Util. Math. 69 (2006) 13-32.
• [6] G. Chartrand, M.S. Jacobson, J. Lehel, O.R. Oellermann, S. Ruiz and F. Saba, Irregular networks, Congress. Numer. 64 (1988) 197-210.
• [7] G. Chartrand and L. Lesniak, Graphs & Digraphs: Fourth Edition (Chapman & Hall/CRC, Boca Raton, FL, 2005).
• [8] G. Chartrand, L. Lesniak, D.W. VanderJagt and P. Zhang, Recognizable colorings of graphs, Discuss. Math. Graph Theory 28 (2008) 35-57, doi: 10.7151/dmgt.1390.
• [9] F. Harary and M. Plantholt, The point-distinguishing chromatic index, in: Graphs and Applications (Wiley, New York, 1985) 147-162.
Typ dokumentu
Bibliografia
Identyfikatory