Wyniki wyszukiwania

Wyszukiwano:
w słowach kluczowych: recognizable coloring

Sortuj według:

Ogranicz wyniki do:

Artykuł dostępny w postaci pełnego tekstu - kliknij by otworzyć plik

Recognizable colorings of graphs

100%

Chartrand G., Lesniak L., VanderJagt D., Zhang P.

Discussiones Mathematicae Graph Theory

2008

tom 28

nr 1

35-57

Let G be a connected graph and let c:V(G) → {1,2,...,k} be a coloring of the vertices of G for some positive integer k (where adjacent vertices may be colored the same). The color code of a vertex v of G (with respect to c) is the ordered (k+1)-tuple code(v) = (a₀,a₁,...,aₖ) where a₀ is the color assigned to v and for 1 ≤ i ≤ k, $a_i$ is the number of vertices adjacent to v that are colored i. The coloring c is called recognizable if distinct vertices have distinct color codes and the recognition number rn(G) of G is the minimum positive integer k for which G has a recognizable k-coloring. Recognition numbers of complete multipartite graphs are determined and characterizations of connected graphs of order n having recognition numbers n or n-1 are established. It is shown that for each pair k,n of integers with 2 ≤ k ≤ n, there exists a connected graph of order n having recognition number k. Recognition numbers of cycles, paths, and trees are investigated.

Recognizable colorings of cycles and trees

100%

Dorfling M., Dorfling S.

Discussiones Mathematicae Graph Theory

2012

tom 32

nr 1

81-90

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.

Ograniczanie wyników

2 Discussiones Mathematicae Graph Theory

1 Chartrand G.

1 Dorfling M.

1 Dorfling S.

1 Lesniak L.

1 VanderJagt D.

1 Zhang P.

1 2012

1 2008

Wyniki wyszukiwania

Recognizable colorings of graphs

Recognizable colorings of cycles and trees