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Total k-domination in Cartesian product graphs [PDF]
, 2017 summary:Let $G$ be a $3$-connected triangulated disc of order $n$ with the boundary cycle $C$ of the outer face of $G$. Tokunaga (2013) conjectured that $G$ has a dominating set of cardinality at most $\frac 14(n+2)$.
Abd Aziz, Noor A'lawiah +5 more
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Disjunctive total domination in graphs [PDF]
Journal of Combinatorial Optimization, 2014 Let $G$ be a graph with no isolated vertex. In this paper, we study a parameter that is a relaxation of arguably the most important domination parameter, namely the total domination number, $γ_t(G)$. A set $S$ of vertices in $G$ is a disjunctive total dominating set of $G$ if every vertex is adjacent to a vertex of $S$ or has at least two vertices in ...
Michael A. Henning, Viroshan Naicker
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On total domination and total equitable domination in graphs
Malaya Journal of Matematik, 2018 A dominating set $D$ of a graph $G$ is called total if every vertex of $V(G)$ is adjacent to at least one vertex of $D$, equivalently if $N(D)=V(G)$ then $D$ is called total dominating set. A dominating set $D$ is called total equitable dominating set if it is total and for every vertex in $V(G)-D$ there exists a vertex in $D$ such that they are ...
null S. K. Vaidya, null A. D. Parmar
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Further Results on the Total Roman Domination in Graphs
Mathematics, 2020 Let G be a graph without isolated vertices. A function f : V ( G ) → { 0 , 1 , 2 } is a total Roman dominating function on G if every vertex v ∈ V ( G ) for which f ( v ) = 0 is adjacent to at least one vertex u ...
Abel Cabrera Martínez +2 more
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Total Domination in Partitioned Graphs [PDF]
Graphs and Combinatorics, 2009 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Frendrup, Allan +2 more
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Total Domination Stable Graphs [PDF]
, 2019 In this paper, we study the total domination number and total domination polynomials of some graph and its square. We discuss nonzero real total domination roots of these graphs.
Shyama M.P., Anil Kumar V.
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Equality of total domination and chromatic total domination in graphs
International journal of health sciences, 2022 Let be a simple, finite and undirected graph and without isolated vertex. A subset D of V is said to be dominating set if for every in there exist a vertex in such that and are adjacent. The minimum cardinality of a dominating set of is called the domination number of and is denoted by .
M. Angala Eswari, S. Balamurugan
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On signed majority total domination in graphs [PDF]
, 2005 summary:We initiate the study of signed majority total domination in graphs. Let $G=(V,E)$ be a simple graph. For any real valued function $f\: V \rightarrow \mathbb{R}$ and ${S\subseteq V}$, let $f(S)=\sum _{v\in S}f(v)$.
Sun, Liang +2 more
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Total domination versus paired domination [PDF]
Discussiones Mathematicae Graph Theory, 2012 A dominating set of a graph G is a vertex subset that any vertex of G either belongs to or is adjacent to. A total dominating set is a dominating set whose induced subgraph does not contain isolated vertices. The minimal size of a total dominating set, the total domination number, is denoted by t.
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Trees with equal total domination and total restrained domination numbers [PDF]
, 2008 For a graph G = (V,E), a set S ⊆ V(G) is a total dominating set if it is dominating and both ⟨S⟩ has no isolated vertices. The cardinality of a minimum total dominating set in G is the total domination number.
Shiu, Wai, Chen, Hong-Yu, Chen, Xue-Gang
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