- Tytuł:
- Defining sets in (proper) vertex colorings of the Cartesian product of a cycle with a complete graph
- Autorzy:
- Mojdeh, D.
- Powiązania:
- https://bibliotekanauki.pl/articles/743869.pdf
- Data publikacji:
- 2006
- Wydawca:
- Uniwersytet Zielonogórski. Wydział Matematyki, Informatyki i Ekonometrii
- Tematy:
-
graph coloring
defining set
cartesian product - Opis:
-
In a given graph G = (V,E), a set of vertices S with an assignment of colors to them is said to be a defining set of the vertex coloring of G, if there exists a unique extension of the colors of S to a c ≥ χ(G) coloring of the vertices of G. A defining set with minimum cardinality is called a minimum defining set and its cardinality is the defining number, denoted by d(G,c).
The d(G = Cₘ × Kₙ, χ(G)) has been studied. In this note we show that the exact value of defining number d(G = Cₘ × Kₙ, c) with c > χ(G), where n ≥ 2 and m ≥ 3, unless the defining number $d(K₃×C_{2r},4)$, which is given an upper and lower bounds for this defining number. Also some bounds of defining number are introduced. - Źródło:
-
Discussiones Mathematicae Graph Theory; 2006, 26, 1; 59-72
2083-5892 - Pojawia się w:
- Discussiones Mathematicae Graph Theory
- Dostawca treści:
- Biblioteka Nauki
Artykuł