منابع مشابه
Total irredundance in graphs
A set S of vertices in a graph G is called a total irredundant set if, for each vertex v in G; v or one of its neighbors has no neighbor in S −{v}. We investigate the minimum and maximum cardinalities of maximal total irredundant sets. c © 2002 Elsevier Science B.V. All rights reserved.
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A set S ⊆ V of vertices in a graph G = (V,E) is called a dominating set if every vertex in V − S is adjacent to at least one vertex in S. Domination in graphs is a well-studied branch of graph theory, and is the subject of two books by Haynes, Hedetniemi and Slater [8, 9]. However, about 90% of the papers on domination have considered only undirected graphs. Thus, relatively little is known abo...
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A set D ⊆ V of vertices is said to be a (connected) distance k-dominating set of G if the distance between each vertex u ∈ V − D and D is at most k (and D induces a connected graph in G). The minimum cardinality of a (connected) distance k-dominating set in G is the (connected) distance k-domination number of G, denoted by γk(G) (γ c k (G), respectively). The set D is defined to be a total k-do...
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Each king on an n×n chessboard is said to attack its own square and its neighboring squares, i.e., the nine or fewer squares within one move of the king. A set of kings is said to form an irredundant set if each attacks a square attacked by no other king in the set. We prove that the maximum size of an irredundant set of kings is bounded between (n− 1)=3 and n=3, and that the minimum size of a ...
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For each vertex s of the vertex subset S of a simple graph G, we define Boolean variables p = p(s, S), q = q(s, S) and r = r(s, S) which measure existence of three kinds of S-private neighbours (S-pns) of s. A 3-variable Boolean function f = f(p, q, r) may be considered as a compound existence property of S-pns. The subset S is called an f -set of G if f = 1 for all s ∈ S and the class of f -se...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 1998
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(97)00098-8