منابع مشابه
Hereditary dominating pair graphs
An asteroidal triple (AT) is a set of vertices such that each pair of vertices is joined by a path that avoids the neighborhood of the third. Every AT-free graph contains a dominating pair, a pair of vertices such that for every path between them, every vertex of the graph is within distance one of the path. We say that a graph is a hereditary dominating pair (HDP) graph if each of its connecte...
متن کاملDominating Pair Graphs
A pair of vertices of a graph is called a dominating pair if the vertex set of every path between these two vertices is a dominating set of the graph. A graph is a weak dominating pair graph if it has a dominating pair. Further, a graph is called a dominating pair graph if each of its connected induced subgraphs is a weak dominating pair graph. Dominating pair graphs form a class of graphs cont...
متن کاملPair dominating graphs
An oriented graph dominates pairs if for every pair of vertices u, v, there exists a vertex w such that the edges ~ wu and ~ wv both lie in G. We construct regular oriented triangle free graphs with this property, and thereby we disprove a conjecture of Myers. We also construct oriented graphs for which each pair of vertices is dominated by a unique vertex.
متن کاملIncidence dominating numbers of graphs
In this paper, the concept of incidence domination number of graphs is introduced and the incidence dominating set and the incidence domination number of some particular graphs such as paths, cycles, wheels, complete graphs and stars are studied.
متن کاملConvex and isometric domination of (weak) dominating pair graphs
A set D of vertices in a graph G is a dominating set if every vertex of G, which is not in D, has a neighbor in D. A set of vertices D in G is convex (respectively, isometric), if all vertices in all shortest paths (respectively, all vertices in one of the shortest paths) between any two vertices in D lie in D. The problem of finding a minimum convex dominating (respectively, isometric dominati...
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ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 2006
ISSN: 0195-6698
DOI: 10.1016/j.ejc.2004.04.016