Results 271 to 280 of about 1,521,521 (318)

A new lower bound on the total domination number of a graph

Quaestiones Mathematicae. Journal of the South African Mathematical Society, 2022
A set S of vertices in a graph G is a total dominating set of G if every vertex in G is adjacent to some vertex in S. The total domination number, γt (G), is the minimum cardinality of a total dominating set of G. Chellali and Haynes [J. Combin.
Majid Hajian, Michael A. Henning, N. J. Rad   +2 more
semanticscholar   +1 more source

Total Domination Edge Critical Graphs with Total Domination Number Three and Many Dominating Pairs

Graphs and Combinatorics, 2014
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Balbuena, Camino, Hansberg, Adriana, Haynes, Teresa W., Henning, Michael A.   +3 more
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Trees with the total domination number twice the distance-2 domination number

, 2021
The distance between two vertices u and v in a graph equals the length of a shortest path from u to v. The distance-2 domination number of a graph G, denoted by γ2(G), is the minimum cardinality of a vertex subset where every vertex not belonging to the ...
Min-Jen Jou, Jenq-Jong Lin, Qian-Yu Lin
semanticscholar   +1 more source

Disjunctive Total Domination Subdivision Number of Graphs

Fundamenta Informaticae, 2020
A set S ⊆ V (G) is a disjunctive total dominating set of G if every vertex has a neighbor in S or has at least two vertices in S at distance 2 from it. The disjunctive total domination number is the minimum cardinality of a disjunctive total dominating set in G. We define the disjunctive total domination subdivision number of G as the minimum number of
Ciftci, Canan, Aytac, Vecdi
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Domination number of total graphs

Mathematica Slovaca, 2016
Abstract Let R be a commutative ring with Z(R) the set of zero-divisors and U(R) the set of unit elements of R. The total graph of R, denoted by T(Γ(R)), is the (undirected) graph with all elements of R as vertices, and for distinct x, y ∈ R, the vertices x and y are adjacent if and only if x + y ∈ Z(R). We study the domination number of
Shariatinia, A., Maimani, H., Yassemi, S.   +2 more
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An algorithm to check the equality of total domination number and double of domination number in graphs

Turkish Journal of Mathematics, 2020
: In graph theory, domination number and its variants such as total domination number are studied by many authors. Let the domination number and the total domination number of a graph G without isolated vertices be γ ( G ) and γ t ( G ) , respectively ...
Selim Bahadır
semanticscholar   +1 more source

Total and Paired Domination Numbers of Cylinders

Bulletin of the Malaysian Mathematical Sciences Society, 2022
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Total Dominator Total Chromatic Numbers of Some Graphs

Utilitas Mathematica
Total dominator total coloring of a graph is a total coloring of the graph such that each object of the graph is adjacent or incident to every object of some color class. The minimum namber of the color classes of a total dominator total coloring of a graph is called the total dominator total chromatic number of the graph.
Vusuqi, Leila, Kazemi, Adel P., Kazemnejad, Farshad   +2 more
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Sharp Upper Bound for Harmonic Index of Trees with Given Total Domination Number

Ars Comb.
Let \( G=(V,E) \) be a simple connected graph with vertex set \( G \) and edge set \( E \). The harmonic index of graph \( G \) is the value \( H(G)=\sum_{uv\in E(G)} \frac{2}{d_u+d_v} \), where \( d_x \) refers to the degree of \( x \).
R. Hasni, Fateme Movahedi, H. Kamarulhaili, M. Akhbari   +3 more
semanticscholar   +1 more source

Total Domination Number Versus Matching Number

2013
In the metadata of the chapter that will be visualized online, please make the following change: “In this chapter, we relate the total domination number of a graph with its matching number”
Michael A. Henning, Anders Yeo
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