Results 61 to 70 of about 259 (109)
On Nordhaus-Gaddum type relations of δ-complement graphs. [PDF]
Heliyon, 2023 Vichitkunakorn P +2 more
europepmc +1 more source
The security number of lexicographic products
, 2018 A subset S of vertices of a graph G is a secure set if |N[X] ∩ S| ≥ |N[X]−S| holds for any subset X of S, where N[X] denotes the closed neighborhood of X. The minimum cardinality s(G) of a secure set in G is called the security number of G.
Gologranc, Tanja +2 more
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On Accurate Domination in Graphs
Discussiones Mathematicae Graph Theory, 2019 A dominating set of a graph G is a subset D ⊆ VG such that every vertex not in D is adjacent to at least one vertex in D. The cardinality of a smallest dominating set of G, denoted by γ(G), is the domination number of G. The accurate domination number of
Cyman Joanna +2 more
doaj +1 more source
Eternal Domination: Criticality and Reachability
Discussiones Mathematicae Graph Theory, 2017 We show that for every minimum eternal dominating set, D, of a graph G and every vertex v ∈ D, there is a sequence of attacks at the vertices of G which can be defended in such a way that an eternal dominating set not containing v is reached.
Klostermeyer William F. +1 more
doaj +1 more source
On the spectrum, energy and Laplacian energy of graphs with self-loops. [PDF]
Heliyon, 2023 Preetha P U, Suresh M, Bonyah E.
europepmc +1 more source
Three-arc graphs: characterization and domination
, 2014 An arc of a graph is an oriented edge and a 3-arc is a 4-tuple (v, u, x, y) of vertices such that both (v, u, x) and (u, x, y) are paths of length two. The 3-arc graph of a graph G is defined to have vertices the arcs of G such that two arcs uv, xy are ...
Guangjun Xu, Sanming Zhou
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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 +1 more source
, 2015 Let G = (V; E) be a graph. A subset D of V is called common neighbourhood dominating set (CN-domi-nating set) if for every v 2 V D there exists a vertex u 2 D such that uv 2 E(G) and j(u; v)j> 1, where j(u; v)j is the number of common neighbourhood ...
N. D. Soner, A. Alwardi
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Total Domination Versus Paired-Domination in Regular Graphs
Discussiones Mathematicae Graph Theory, 2018 A subset S of vertices of a graph G is a dominating set of G if every vertex not in S has a neighbor in S, while S is a total dominating set of G if every vertex has a neighbor in S. If S is a dominating set with the additional property that the subgraph
Cyman Joanna +4 more
doaj +1 more source
On the sum of the total domination numbers of a diagraph and its converse
, 2019 A vertex subset S of a digraph D is called a dominating set of D if every vertex not in S has an in-neighbor in S. A dominating set S of D is called a total dominating set of D if the subdigraph induced by S has no isolated vertices. The total domination
Xie, Zhihong +2 more
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