منابع مشابه
Generalized connected domination in graphs
As a generalization of connected domination in a graph G we consider domination by sets having at most k components. The order γ c (G) of such a smallest set we relate to γc(G), the order of a smallest connected dominating set. For a tree T we give bounds on γ c (T ) in terms of minimum valency and diameter. For trees the inequality γ c (T ) ≤ n− k − 1 is known to hold, we determine the class o...
متن کاملDomination Value in Graphs
A set D ⊆ V (G) is a dominating set of G if every vertex not in D is adjacent to at least one vertex in D. A dominating set of G of minimum cardinality is called a γ(G)-set. For each vertex v ∈ V (G), we define the domination value of v to be the number of γ(G)-sets to which v belongs. In this paper, we study some basic properties of the domination value function, thus initiating a local study ...
متن کاملConnected domination of regular graphs
A dominating set D of a graph G is a subset of V (G) such that for every vertex v ∈ V (G), either v ∈ D or there exists a vertex u ∈ D that is adjacent to v in G. Dominating sets of small cardinality are of interest. A connected dominating set C of a graph G is a dominating set of G such that the subgraph induced by the vertices of C in G is connected. A weakly-connected dominating set W of a g...
متن کاملOn Domination in 2-Connected Cubic Graphs
In 1996, Reed proved that the domination number, γ(G), of every n-vertex graph G with minimum degree at least 3 is at most 3n/8 and conjectured that γ(H) ≤ dn/3e for every connected 3-regular (cubic) n-vertex graph H. In [1] this conjecture was disproved by presenting a connected cubic graph G on 60 vertices with γ(G) = 21 and a sequence {Gk} ∞ k=1 of connected cubic graphs with limk→∞ γ(Gk) |V...
متن کاملOuter-k-connected component domination in graphs
A subset S of the vertices of a graph G is an outer-connected dominating set, if S is a dominating set of G and G − S is connected. The outer-connected domination number of G, denoted by γ̃c(G), is the minimum cardinality of an OCDS of G. In this paper we generalize the outer-connected domination in graphs. Many of the known results and bounds of outer-connected domination number are immediate c...
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ژورنال
عنوان ژورنال: Electronic Journal of Graph Theory and Applications
سال: 2021
ISSN: 2338-2287
DOI: 10.5614/ejgta.2021.9.1.11