Results 1 to 10 of about 1,294 (93)
Reinforcement Number of a Graph with respect to Half-Domination
Journal of Mathematics, 2021 In this paper, we introduce the concept of reinforcement number with respect to half-domination and initiate a study on this parameter. Furthermore, we obtain various upper bounds for this parameter. AMS subject classification: 05C38, 05C40, 05C69.
G. Muhiuddin +4 more
doaj +2 more sources
Relating the super domination and 2-domination numbers in cactus graphs
Open Mathematics, 2023 A set D⊆V(G)D\subseteq V\left(G) is a super dominating set of a graph GG if for every vertex u∈V(G)\Du\in V\left(G)\setminus D, there exists a vertex v∈Dv\in D such that N(v)\D={u}N\left(v)\setminus D=\left\{u\right\}.
Cabrera-Martínez Abel +1 more
doaj +1 more source
Further Results on Packing Related Parameters in Graphs
Discussiones Mathematicae Graph Theory, 2022 Given a graph G = (V, E), a set B ⊆ V (G) is a packing in G if the closed neighborhoods of every pair of distinct vertices in B are pairwise disjoint. The packing number ρ(G) of G is the maximum cardinality of a packing in G. Similarly, open packing sets
Mojdeh Doost Ali +2 more
doaj +1 more source
A Classification of Cactus Graphs According to their Domination Number
Discussiones Mathematicae Graph Theory, 2022 A set S of vertices in a graph G is a dominating set of G if every vertex not in S is adjacent to some vertex in S. The domination number, γ(G), of G is the minimum cardinality of a dominating set of G.
Hajian Majid +2 more
doaj +1 more source
Roman {2}-Domination Problem in Graphs
Discussiones Mathematicae Graph Theory, 2022 For a graph G = (V, E), a Roman {2}-dominating function (R2DF) f : V → {0, 1, 2} has the property that for every vertex v ∈ V with f(v) = 0, either there exists a neighbor u ∈ N(v), with f(u) = 2, or at least two neighbors x, y ∈ N(v) having f(x) = f(y) =
Chen Hangdi, Lu Changhong
doaj +1 more source
On a Vizing-type integer domination conjecture [PDF]
, 2020 Given a simple graph $G$, a dominating set in $G$ is a set of vertices $S$ such that every vertex not in $S$ has a neighbor in $S$. Denote the domination number, which is the size of any minimum dominating set of $G$, by $\gamma(G)$.
Davila, Randy, Krop, Elliot
core +3 more sources
Domination Number, Independent Domination Number and 2-Independence Number in Trees
Discussiones Mathematicae Graph Theory, 2021 For a graph G, let γ(G) be the domination number, i(G) be the independent domination number and β2(G) be the 2-independence number. In this paper, we prove that for any tree T of order n ≥ 2, 4β2(T) − 3γ(T) ≥ 3i(T), and we characterize all trees ...
Dehgardi Nasrin +4 more
doaj +1 more source
Restrained Domination in Self-Complementary Graphs
Discussiones Mathematicae Graph Theory, 2021 A self-complementary graph is a graph isomorphic to its complement. A set S of vertices in a graph G is a restrained dominating set if every vertex in V(G) \ S is adjacent to a vertex in S and to a vertex in V(G) \ S.
Desormeaux Wyatt J. +2 more
doaj +1 more source
Total Dominator Colorings in Cycles [PDF]
, 2012 Determining the total dominator chromatic number in ...
Vijayalekshmi, A.
core +2 more sources
Total Domination in Generalized Prisms and a New Domination Invariant
Discussiones Mathematicae Graph Theory, 2021 In this paper we complement recent studies on the total domination of prisms by considering generalized prisms, i.e., Cartesian products of an arbitrary graph and a complete graph.
Tepeh Aleksandra
doaj +1 more source