منابع مشابه
Domination dot-critical graphs
A graph G is dot-critical if contracting any edge decreases the domination number. It is totally dot-critical if identifying any two vertices decreases the domination number. We show that the totally dot-critical graphs essentially include the much-studied domination vertex-critical and edge-critical graphs as special cases. We investigate these properties, and provide a characterization of dot...
متن کاملLocating-total domination critical graphs
A locating-total dominating set of a graph G = (V (G), E(G)) with no isolated vertex is a set S ⊆ V (G) such that every vertex of V (G) is adjacent to a vertex of S and for every pair of distinct vertices u and v in V (G) − S, N(u) ∩ S = N(v) ∩ S. Let γ t (G) be the minimum cardinality of a locating-total dominating set of G. A graph G is said to be locating-total domination vertex critical if ...
متن کاملtotal $k$-distance domination critical graphs
a set $s$ of vertices in a graph $g=(v,e)$ is called a total$k$-distance dominating set if every vertex in $v$ is withindistance $k$ of a vertex in $s$. a graph $g$ is total $k$-distancedomination-critical if $gamma_{t}^{k} (g - x) < gamma_{t}^{k}(g)$ for any vertex $xin v(g)$. in this paper,we investigate some results on total $k$-distance domination-critical of graphs.
متن کاملDomination dot-critical graphs with no critical vertices
A graph G is dot-critical if contracting any edge decreases the domination number. It is totally dot-critical if identifying any two vertices decreases the domination number. Burton and Sumner [Discrete Math. 306 (2006) 11–18] posed the problem: Is it true that for k 4, there exists a totally k-dot-critical graph with no critical vertices? In this paper, we show that this problem has a positive...
متن کاملTOTAL k-DISTANCE DOMINATION CRITICAL GRAPHS
A set S of vertices in a graph G = (V,E) is called a total k-distance dominating set if every vertex in V is within distance k of a vertex in S. A graph G is total k-distance domination-critical if γ t (G − x) < γ t (G) for any vertex x ∈ V (G). In this paper, we investigate some results on total k-distance domination-critical of graphs.
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2011
ISSN: 0166-218X
DOI: 10.1016/j.dam.2010.10.006