منابع مشابه
Minimum Span of No-Hole (r+1)-Distant Colorings
Given a nonnegative integer r, a no-hole (r+1)-distant coloring, called Nr-coloring, of a graph G is a function that assigns a nonnegative integer (color) to each vertex such that the separation of the colors of any pair of adjacent vertices is greater than r, and the set of the colors used must be consecutive. Given r and G, the minimum Nr-span of G, nspr(G), is the minimum difference of the l...
متن کاملNo-hole L(2, 1)-colorings
An L(2, 1)-coloring of a graph G is a coloring of G’s vertices with integers in {0, 1, . . . , k} so that adjacent vertices’ colors differ by at least two and colors of distance-two vertices differ. We refer to an L(2, 1)-coloring as a coloring. The span λ(G) of G is the smallest k for which G has a coloring, a span coloring is a coloring whose greatest color is λ(G), and the hole index ρ(G) of...
متن کاملNo-hole 2-distant colorings for Cayley graphs on finitely generated abelian groups
A no-hole 2-distant coloring of a graph is an assignment c of nonnegative integers to the vertices of such that |c(v)−c(w)| 2 for any two adjacent vertices v and w, and the integers used are consecutive. Whenever such a coloring exists, define nsp( ) to be the minimum difference (over all c) between the largest and smallest integers used. In this paper we study the no-hole 2-distant coloring pr...
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This paper studies proper k-tuple edge-colorings of graphs that distinguish neighboring vertices by their sets of colors. Minimum number of colors for such colorings are determined for cycles, complete graphs and complete bipartite graphs. A variation in which the color sets assigned to edges have to form cyclic intervals is also studied and similar results are given.
متن کاملk-TUPLE DOMATIC IN GRAPHS
For every positive integer k, a set S of vertices in a graph G = (V;E) is a k- tuple dominating set of G if every vertex of V -S is adjacent to at least k vertices and every vertex of S is adjacent to at least k - 1 vertices in S. The minimum cardinality of a k-tuple dominating set of G is the k-tuple domination number of G. When k = 1, a k-tuple domination number is the well-studied domination...
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 1996
ISSN: 0166-218X
DOI: 10.1016/0166-218x(94)00030-h