Results 21 to 30 of about 9,132,004 (247)

Total domination subdivision numbers of trees

Discrete Mathematics, 2004
The total domination subdivision number \(\text{ sd}_{\gamma_t}(G)\) of a graph \(G\) is the minimum number of edges whose subdivision increases the total domination number \({\gamma_t}(G)\) of \(G\). \textit{T. W. Haynes} et al. [J. Comb. Math. Comb. Comput.
Teresa W. Haynes, Michael A. Henning, Lora Hopkins   +2 more
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On total domination subdivision numbers of trees [PDF]

Discussiones Mathematicae Graph Theory
15 pages, 7 ...
Michael A. Henning, Jerzy Topp
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DOMINATION NUMBER AND WATCHING NUMBER OF SUBDIVISION CONSTRUCTION OF GRAPHS [PDF]

Facta Universitatis, Series: Mathematics and Informatics
In light of the results of a domination number of the subdivision of a graph G, we determine an upper bound of the watching number of S(G). In addition, we obtain a condition with which the upper bound becomes sharp.
Kamran Mirasheh, Ahmad Abbasi, Ebrahim Vatandoost   +2 more
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DOMINATION NUMBER AND IDENTIFYING CODE NUMBER OF THE SUBDIVISION GRAPHS [PDF]

Journal of Algebraic Systems
‎Let $G=(V‎, ‎E)$ be a simple graph‎. ‎A set $C$ of vertices of $G$ is an identifying code of $G$ if for every two vertices $x$ and $y$ the sets $N_{G}[x] \cap C$ and $N_{G}[y] \cap C$ are non-empty and different‎.
Somaiya Ahmadi, Ebrahim Vatandoost, Ali Behtoei   +2 more
doaj   +2 more sources

Total $k$-rainbow domination subdivision number in graphs [PDF]

Computer Science Journal of Moldova, 2020
A total $k$-rainbow dominating function (T$k$RDF) of $G$ is a function $f$ from the vertex set $V(G)$ to the set of all subsets of the set $\{1,\ldots,k\}$ such that (i) for any vertex $v\in V(G)$ with $f(v)=\emptyset$ the condition $\bigcup_{u \in N(v ...
Rana Khoeilar, Mahla Kheibari, Zehui Shao, Seyed Mahmoud Sheikholeslami   +3 more
doaj   +3 more sources

Algorithmic Complexity and Bounds for Domination Subdivision Numbers of Graphs

Journal of Mathematics
Let G=V,E be a simple graph. A subset D⊆V is a dominating set if every vertex not in D is adjacent to a vertex in D. The domination number of G, denoted by γG, is the smallest cardinality of a dominating set of G.
Fu-Tao Hu, Chang-Xu Zhang, Shu-Cheng Yang   +2 more
doaj   +2 more sources

On the total domination subdivision numbers in graphs

Open Mathematics, 2010
Abstract A set S of vertices of a graph G = (V, E) without isolated vertex is a total dominating set if every vertex of V(G) is adjacent to some vertex in S. The total domination number γ t(G) is the minimum cardinality of a total dominating set of G. The total domination subdivision number sdγt
Sheikholeslami Seyed
doaj   +3 more sources

Coronas and Domination Subdivision Number of a Graph [PDF]

Bulletin of the Malaysian Mathematical Sciences Society, 2016
In this paper, for a graph G and a family of partitions P of vertex neighborhoods of G, we define the general corona G \circ P of G. Among several properties of this new operation, we focus on application general coronas to a new kind of characterization of trees with the domination subdivision number equal to 3.
Magda Dettlaff, Magdalena Lemańska, Jerzy Topp, Paweł Żyliński   +3 more
openaire   +4 more sources

The Forcing Domination Number of Hamiltonian Cubic Graphs [PDF]

, 2009
The authors presented a sequence of Hamiltonian cubic graphs whose domination numbers are sharp and in this paper we study forcing domination number for those ...
H. Abdollahzadeh Ahangar, H.Abdollahzadeh Ahangar, Abdollahzadeh Ahangar, H., Pushpalatha L.   +3 more
core   +1 more source

Changing of the domination number of a graph: edge multisubdivision and edge removal [PDF]

Mathematica Bohemica, 2017
For a graphical property $\mathcal{P}$ and a graph $G$, a subset $S$ of vertices of $G$ is a $\mathcal{P}$-set if the subgraph induced by $S$ has the property $\mathcal{P}$.
Vladimir Samodivkin
doaj   +1 more source