Domination parameters of a graph and its complement
نویسندگان
چکیده
منابع مشابه
Signed domination numbers of a graph and its complement
Let G = (V, E) be a simple graph on vertex set V and define a function f : V → {−1, 1}. The function f is a signed dominating function if for every vertex x ∈ V , the closed neighborhood of x contains more vertices with function value 1 than with −1. The signed domination number of G, γs(G), is the minimum weight of a signed dominating function on G. Let G denote the complement of G. In this pa...
متن کاملPaired-domination number of a graph and its complement
A paired-dominating set of a graph G = (V, E) with no isolated vertex is a dominating set of vertices inducing a graph with a perfect matching. The paired-domination number of G, denoted by γpr (G), is the minimum cardinality of a paired-dominating set of G. We consider graphs of order n ≥ 6, minimum degree δ such that G and G do not have an isolated vertex and we prove that – if γpr (G) > 4 an...
متن کاملConnected Domination Number of a Graph and its Complement
A set S of vertices in a graph G is a connected dominating set if every vertex not in S is adjacent to some vertex in S and the subgraph induced by S is connected. The connected domination number γc(G) is the minimum size of such a set. Let δ(G) = min{δ(G), δ(G)}, where G is the complement of G and δ(G) is the minimum vertex degree. We prove that when G and G are both connected, γc(G) + γc(G) ≤...
متن کاملNeighborhood total domination of a graph and its complement
A neighborhood total dominating set in a graph G is a dominating set S of G with the property that the subgraph induced by N(S), the open neighborhood of the set S, has no isolated vertex. The neighborhood total domination number γnt(G) is the minimum cardinality of a neighborhood total dominating set of G. Arumugam and Sivagnanam introduced and studied the concept of neighborhood total dominat...
متن کاملTotal domination and total domination subdivision number of a graph and its complement
A set S of vertices of a graph G= (V ,E) with no isolated vertex is a total dominating set if every vertex of V (G) is adjacent to some vertex in S. The total domination number t(G) is the minimum cardinality of a total dominating set ofG. The total domination subdivision number sd t (G) is the minimum number of edges that must be subdivided in order to increase the total domination number. We ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Discussiones Mathematicae Graph Theory
سال: 2018
ISSN: 1234-3099,2083-5892
DOI: 10.7151/dmgt.2002