Complementary Tree Domination Number of a Graph
نویسنده
چکیده
A set D of a graph G = (V,E) is a dominating set if every vertex in V −D is adjacent to some vertex in D. The domination number γ(G) of G is the minimum cardinality of a dominating set. A dominating set D is called a complementary tree dominating set if the induced sub graph < V −D > is a tree. The minimum cardinality of a complementary tree dominating set is called the complementary tree domination number of G and is denoted by γctd(G). In this paper, bounds for γctd(G) and its exact values for some particular classes of graphs are found. Some results on complementary tree domination number are also established. Mathematics Subject Classification: 05C69
منابع مشابه
On trees attaining an upper bound on the total domination number
A total dominating set of a graph $G$ is a set $D$ of vertices of $G$ such that every vertex of $G$ has a neighbor in $D$. The total domination number of a graph $G$, denoted by $gamma_t(G)$, is~the minimum cardinality of a total dominating set of $G$. Chellali and Haynes [Total and paired-domination numbers of a tree, AKCE International ournal of Graphs and Combinatorics 1 (2004), 6...
متن کاملBounds on the outer-independent double Italian domination number
An outer-independent double Italian dominating function (OIDIDF)on a graph $G$ with vertex set $V(G)$ is a function$f:V(G)longrightarrow {0,1,2,3}$ such that if $f(v)in{0,1}$ for a vertex $vin V(G)$ then $sum_{uin N[v]}f(u)geq3$,and the set $ {uin V(G)|f(u)=0}$ is independent. The weight ofan OIDIDF $f$ is the value $w(f)=sum_{vin V(G)}f(v)$. Theminimum weight of an OIDIDF on a graph $G$ is cal...
متن کاملChanging and Unchanging of Complementary Tree Domination Number in Graphs
A set D of a graph G = (V,E) is a dominating set if every vertex in V −D is adjacent to some vertex in D. The domination number γ(G) of G is the minimum cardinality of a dominating set. A dominating set D is called a complementary tree dominating set if the induced subgraph < V −D > is a tree. The minimum cardinality of a complementary tree dominating set is called the complementary tree domina...
متن کاملComplementary Tree Domination in Splitting Graphs of Graphs
Let G = (V, E) be a simple graph. A dominating set D is called a complementary tree dominating set if the induced subgraph is a tree. The minimum cardinality of a complementary tree dominating set is called the complementary tree domination number of G and is denoted by ctd(G). For a graph G, let V(G) = {v : v V(G)} be a copy of V(G). The splitting graph Sp(G) of G is the graph with ...
متن کاملRoman domination excellent graphs: trees
A Roman dominating function (RDF) on a graph $G = (V, E)$ is a labeling $f : V rightarrow {0, 1, 2}$ suchthat every vertex with label $0$ has a neighbor with label $2$. The weight of $f$ is the value $f(V) = Sigma_{vin V} f(v)$The Roman domination number, $gamma_R(G)$, of $G$ is theminimum weight of an RDF on $G$.An RDF of minimum weight is called a $gamma_R$-function.A graph G is said to be $g...
متن کامل