منابع مشابه
Factor d-domatic colorings of graphs
Consider a graph and a collection of (not necessarily edge-disjoint) connected spanning subgraphs (factors) of the graph. We consider the problem of coloring the vertices of the graph so that each color class of the vertices dominates each factor. We find upper and lower bounds on α(t, k), which we define as the minimum radius of domination d such that every graph with a collection of k factors...
متن کاملD-strong Total Colorings of Graphs
If c : V ∪ E → {1, 2, . . . , k} is a proper total coloring of a graph G = (V,E) then the palette S[v] of a vertex v ∈ V is the set of colors of the incident edges and the color of v: S[v] = {c(e) : e = vw ∈ E} ∪ {c(v)}. A total coloring c distinguishes vertices u and v if S[u] 6= S[v]. A d-strong total coloring of G is a proper total coloring that distinguishes all pairs of vertices u and v wi...
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In this paper, we enumerate the parameter matrices of all perfect $2$-colorings of the Platonic graphs consisting of the tetrahedral graph, the cubical graph, the octahedral graph, the dodecahedral graph, and the icosahedral graph.
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...
متن کاملDomatic partitions of computable graphs
Given a graph G, we say that a subset D of the vertex set V is a dominating set if it is near all the vertices, in that every vertex outside of D is adjacent to a vertex in D. A domatic k-partition of G is a partition of V into k dominating sets. In this paper, we will consider issues of computability related to domatic partitions of computable graphs. Our investigation will center on answering...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2003
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(02)00518-6