Results 1 to 10 of about 1,374,871 (283)
Some results on the open locating-total domination number in graphs [PDF]
Journal of Mahani Mathematical Research, 2023 In this paper, we generalize the concept of an open locating-dominating set in graphs. We introduce a concept as an open locating-total dominating set in graphs that is equivalent to the open neighborhood locating-dominating set.
Fateme Movahedi, Mohammad Hadi Akhbari
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Effect of predomination and vertex removal on the game total domination number of a graph [PDF]
Discrete Applied Mathematics, 2018 The game total domination number, ${\gamma_{g}^{t}}$, was introduced by Henning et al.\ in 2015. In this paper we study the effect of vertex predomination on the game total domination number. We prove that ${\gamma_{g}^{t}}(G|v) \geq {\gamma_{g}^{t}}(G) -
Vesna Iršič
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On the Quasi-Total Roman Domination Number of Graphs
Mathematics, 2021 Domination theory is a well-established topic in graph theory, as well as one of the most active research areas. Interest in this area is partly explained by its diversity of applications to real-world problems, such as facility location problems ...
Abel Cabrera Martínez +2 more
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Graphs with Total Domination Number Double of the Matching Number
Journal of New TheoryA subset $S$ of vertices of a graph $G$ with no isolated vertex is called a total dominating set of $G$ if each vertex of $G$ has at least one neighbor in the set $S$.
Selim Bahadır
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On the inverse signed total domination number in graphs [PDF]
Opuscula Mathematica, 2017 In this paper, we study the inverse signed total domination number in graphs and present new sharp lower and upper bounds on this parameter. For example by making use of the classic theorem of Turán (1941), we present a sharp upper bound on \(K_{r+1 ...
D. A. Mojdeh, B. Samadi
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New Bounds on the Signed Total Domination Number of Graphs
Discussiones Mathematicae Graph Theory, 2016 In this paper, we study the signed total domination number in graphs and present new sharp lower and upper bounds for this parameter. For example by making use of the classic theorem of Turán [8], we present a sharp lower bound on Kr+1-free graphs for r ≥
Moghaddam Seyyed Mehdi Hosseini +3 more
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Outer independent total double Italian domination number [PDF]
Computer Science Journal of MoldovaIf $G$ is a graph with vertex set $V(G)$, then let $N[u]$ be the closed neighborhood of the vertex $u\in V(G)$. A total double Italian dominating function (TDIDF) on a graph $G$ is a function $f:V(G)\rightarrow\{0,1,2,3\}$ satisfying (i) $f(N[u])\ge 3 ...
Seyed Mahmoud Sheikholeslami +1 more
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Total Roman Domination Number of Rooted Product Graphs
Mathematics, 2020 Let G be a graph with no isolated vertex and f:V(G)→{0,1,2} a function. If f satisfies that every vertex in the set {v∈V(G):f(v)=0} is adjacent to at least one vertex in the set {v∈V(G):f(v)=2}, and if the subgraph induced by the set {v∈V(G):f(v)≥1} has ...
Abel Cabrera Martínez +3 more
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On the Secure Total Domination Number of Graphs
Symmetry, 2019 A total dominating set D of a graph G is said to be a secure total dominating set if for every vertex u ∈ V ( G ) \ D , there exists a vertex v ∈ D , which is adjacent to u, such that ( D \ { v } ) ∪ { u } is a total dominating set as well.
Abel Cabrera Martínez +2 more
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Total \(k\)-rainbow domination numbers in graphs
Communications in Combinatorics and Optimization, 2018 Summary: Let \(k\geq 1\) be an integer, and let \(G\) be a graph. A \(k\)-rainbow dominating function (or a \(k\)-RDF) of \(G\) is a function \(f\) from the vertex set \(V(G)\) to the family of all subsets of \({1,2,\ldots ,k}\) such that for every \(v\in V(G)\) with \(f(v)=\emptyset\), the condition \(\bigcup_{u\in N_{G}(v)}f(u)=\{1,2,\ldots,k\}\) is ...
Abdollahzadeh Ahangar, Hossein +3 more
openaire +2 more sources