Total Domination on Some Graph Operators
نویسندگان
چکیده
Let G=(V,E) be a graph; set D⊆V is total dominating if every vertex v∈V has, at least, one neighbor in D. The domination number γt(G) the minimum cardinality among all sets. Given an arbitrary graph G, we consider some operators on this S(G),R(G), and Q(G), give bounds or exact value of these new graphs using parameters original G.
منابع مشابه
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...
متن کاملSome conjectures of Graffiti.pc on total domination
We limit our discussion to graphs that are simple and finite of order . Although 8 we often identify a graph with its set of vertices, in cases where we need to be K explicit we write . A set of vertices of is said to Z ÐKÑ Q K dominate K provided each vertex of is either in or adjacent to a vertex of . K Q Q The domination number of is the minimum order of a dominating set. A K dominating prov...
متن کاملdomination 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(ga...
متن کاملNote: Simultaneous Graph Parameters: Factor Domination and Factor Total Domination
Let F1, F2, . . . , Fk be graphs with the same vertex set V . A subset S ⊆ V is a factor dominating set if in every Fi every vertex not in S is adjacent to a vertex in S, and a factor total dominating set if in every Fi every vertex in V is adjacent to a vertex in S. The cardinality of a smallest such set is the factor (total) domination number. In this note we investigate bounds on the factor ...
متن کاملSimultaneous graph parameters: Factor domination and factor total domination
Let F1, F2, . . . , Fk be graphs with the same vertex set V . A subset S ⊆ V is a factor dominating set if in every Fi every vertex not in S is adjacent to a vertex in S, and a factor total dominating set if in every Fi every vertex in V is adjacent to a vertex in S. The cardinality of a smallest such set is the factor (total) domination number. We investigate bounds on the factor (total) domin...
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: Mathematics
سال: 2021
ISSN: ['2227-7390']
DOI: https://doi.org/10.3390/math9030241