Results 1 to 10 of about 11,485 (159)
Total Domination Multisubdivision Number of a Graph
Discussiones Mathematicae Graph Theory, 2015 The domination multisubdivision number of a nonempty graph G was defined in [3] as the minimum positive integer k such that there exists an edge which must be subdivided k times to increase the domination number of G.
Avella-Alaminos Diana +3 more
doaj +4 more sources
Total domination number of middle graphs
Electronic Journal of Graph Theory and Applications, 2022 A total dominating set of a graph G with no isolated vertices is a subset S of the vertex set such that every vertex of G is adjacent to a vertex in S. The total domination number of G is the minimum cardinality of a total dominating set.
Farshad Kazemnejad +3 more
doaj +4 more sources
Computing locating-total domination number in some rotationally symmetric graphs [PDF]
Science Progress, 2021 Let G = ( V , E ) be a connected graph. A locating-total dominating set in a graph G is a total dominating set S of a G , for every pair of vertices i , j ∈ V ( G ) ∖ S , such that N ( i ) ∩ S ≠ N ( j ) ∩ S .
Hassan Raza +3 more
doaj +2 more sources
On the total domination number of total graphs
Discussiones Mathematicae Graph TheorySummary: Let \(G\) be a graph with no isolated vertex. A set \(D\subseteq V(G)\) is a total dominating set of \(G\) if every vertex of \(G\) is adjacent to at least one vertex in \(D\). The total domination number of \(G\), denoted by \(\gamma_t(G)\), is the minimum cardinality among all total dominating sets of \(G\).
Abel Cabrera-Martínez +2 more
doaj +4 more sources
Bounds on the Locating-Domination Number and Differentiating-Total Domination Number in Trees
Discussiones Mathematicae Graph Theory, 2018 A subset S of vertices in a graph G = (V,E) is a dominating set of G if every vertex in V − S has a neighbor in S, and is a total dominating set if every vertex in V has a neighbor in S.
Rad Nader Jafari, Rahbani Hadi
doaj +2 more sources
Total and Double Total Domination Number on Hexagonal Grid [PDF]
Mathematics, 2019 In this paper, we determine the upper and lower bound for the total domination number and exact values and the upper bound for the double-total domination number on hexagonal grid H m , n with m hexagons in a row and n hexagons in a column ...
Antoaneta Klobučar, Ana Klobučar
doaj +2 more sources
Fair Total Domination Number in Cactus Graphs
Discussiones Mathematicae Graph Theory, 2021 For k ≥ 1, a k-fair total dominating set (or just kFTD-set) in a graph G is a total dominating set S such that |N(v) ∩ S| = k for every vertex v ∈ V\S. The k-fair total domination number of G, denoted by ftdk(G), is the minimum cardinality of a kFTD-set.
Hajian Majid, Rad Nader Jafari
doaj +3 more sources
Graphs with large disjunctive total domination number [PDF]
Discrete Mathematics & Theoretical Computer Science, 2015 Graph ...
Michael A. Henning, Viroshan Naicker
doaj +4 more sources
On Grundy Total Domination Number in Product Graphs
Discussiones Mathematicae Graph Theory, 2021 A longest sequence (v1, . . ., vk) of vertices of a graph G is a Grundy total dominating sequence of G if for all i, N(υj)\∪j=1i-1N(υj)≠∅N({\upsilon _j})\backslash \bigcup\nolimits_{j = 1}^{i - 1} {N({\upsilon _j})} \ne \emptyset .
Brešar Boštjan +8 more
doaj +6 more sources
On a Class of Graphs with Large Total Domination Number [PDF]
Discrete Mathematics & Theoretical Computer Science, 2018 Let $\gamma(G)$ and $\gamma_t(G)$ denote the domination number and the total domination number, respectively, of a graph $G$ with no isolated vertices. It is well-known that $\gamma_t(G) \leq 2\gamma(G)$.
Selim Bahadır, Didem Gözüpek
doaj +7 more sources