Results 61 to 70 of about 1,516 (111)
On the number of outer connected dominating sets of graphs
, 2012 Let $G=(V,E)$ be a simple graph. A set $S\subseteq V(G)$ is called an outer-connected dominating set (or ocd-set) of $G$, if $S$ is a dominating set of $G$ and either $S=V(G)$ or $V\backslash S$ is a connected graph.
Akhbari, Mohammad H. +2 more
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Symmetric Shannon capacity is the independence number minus 1
, 2018 A symmetric variant of Shannon capacity is defined and computed.Comment: 4 pages, submitted to Electronic Journal of ...
Terpai, Tamás
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On Nordhaus-Gaddum type relations of δ-complement graphs. [PDF]
Heliyon, 2023 Vichitkunakorn P +2 more
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Power Domination in the Generalized Petersen Graphs
Discussiones Mathematicae Graph Theory, 2020 The problem of monitoring an electric power system by placing as few measurement devices in the system can be formulated as a power dominating set problem in graph theory.
Zhao Min, Shan Erfang, Kang Liying
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
Factor-Critical Property in 3-Dominating-Critical Graphs
, 2006 A vertex subset $S$ of a graph $G$ is a dominating set if every vertex of $G$ either belongs to $S$ or is adjacent to a vertex of $S$. The cardinality of a smallest dominating set is called the dominating number of $G$ and is denoted by $\gamma(G)$.
Wang, Tao, Yu, Qinglin
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Domination Parameters of a Graph and its Complement
Discussiones Mathematicae Graph Theory, 2018 A dominating set in a graph G is a set S of vertices such that every vertex in V (G) \ S is adjacent to at least one vertex in S, and the domination number of G is the minimum cardinality of a dominating set of G.
Desormeaux Wyatt J. +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
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A construction of small (q-1)-regular graphs of girth 8
, 2015 In this note we construct a new infinite family of $(q-1)$-regular graphs of girth $8$ and order $2q(q-1)^2$ for all prime powers $q\ge 16$, which are the smallest known so far whenever $q-1$ is not a prime power or a prime power plus one itself.Comment:
Abreu, M. +3 more
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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
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