Total domination and total domination subdivision number of a graph and its complement

Total 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 ...

Total Roman domination subdivision number in graphs

A {em Roman dominating function} on a graph $G$ is a function $f:V(G)rightarrow {0,1,2}$ satisfying the condition that every vertex $u$ for which $f(u)=0$ is adjacent to at least one vertex $v$ for which $f(v)=2$. A {em total Roman dominating function} is a Roman dominating function with the additional property that the subgraph of $G$ induced by the set of all vertices of positive weight has n...

DOMINATION NUMBER OF TOTAL GRAPH OF MODULE

 Let $R$ be a commutative ring and $M$ be an $R$-module with $T(M)$ as subset, the set of torsion elements. The total graph of the module denoted by $T(Gamma(M))$, is the (undirected) graph with all elements of $M$ as vertices, and for distinct elements $n,m in M$, the vertices $n$ and $m$ are adjacent if and only if $n+m in T(M)$. In this paper we study the domination number of $T(Gamma(M))$ a...

Total domination and total domination subdivision numbers

Neighborhood 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...