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Graphs with equal domination and independent domination numbers [PDF]
AKCE International Journal of Graphs and Combinatorics, 2020 Let γ(G) and i(G) denote the domination number and independent domination number of a graph G. In this article, we establish a sufficient condition for a graph G to satisfy which yields some of the well known classical theorems as corollaries.
Purnima Gupta, Rajesh Singh, S. Arumugam
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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
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Independent [1,2]-number versus independent domination number [PDF]
Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2017 A [1; 2]-set S in a graph G is a vertex subset such that every vertex not in S has at least one and at most two neighbors in it. If the additional requirement that the set be independent is added, the existence of such sets is not guaranteed in every ...
Aleid Sahar A. +2 more
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Discussiones Mathematicae Graph Theory, 2022 A 2-rainbow dominating function (2RDF) of a graph G is a function g from the vertex set V (G) to the family of all subsets of {1, 2} such that for each vertex v with g(v) =∅ we have ∪u∈N(v) g(u) = {1, 2}.
Poureidi Abolfazl, Rad Nader Jafari
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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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The Domination Parameters on a kind of the regular honeycomb structure [PDF]
Computer Science Journal of Moldova, 2022 The honeycomb mesh, based on hexagonal structure, has enormous applications in chemistry and engineering. A major challenge in this field is to understand the unique properties of honeycomb structures, which depend on their properties of topology. One
Fateme Movahedi +2 more
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Strong Equality Between the Roman Domination and Independent Roman Domination Numbers in Trees
Discussiones Mathematicae Graph Theory, 2013 A Roman dominating function (RDF) on a graph G = (V,E) is a function f : V −→ {0, 1, 2} satisfying the condition that every vertex u for which f(u) = 0 is adjacent to at least one vertex v for which f(v) = 2.
Chellali Mustapha, Rad Nader Jafari
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Remarks on the outer-independent double Italian domination number [PDF]
Opuscula Mathematica, 2021 Let \(G\) be a graph with vertex set \(V(G)\). If \(u\in V(G)\), then \(N[u]\) is the closed neighborhood of \(u\). An outer-independent double Italian dominating function (OIDIDF) on a graph \(G\) is a function \(f:V(G)\longrightarrow \{0,1,2,3\}\) such
Lutz Volkmann
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On the Outer Independent Double Roman Domination Number [PDF]
Bulletin of the Iranian Mathematical Society, 2021 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Doost Ali Mojdeh +3 more
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Independent Restrained k - Rainbow Dominating Function
Ratio Mathematica, 2022 Let G be a graph and let f be a function that assigns to each vertex a set of colors chosen from the set {1, 2…, k} that is f: V(G) P [1,2,…,k]. If for each vertex v V(G) such that f(v) = .we have then f is called the k – Rainbow Dominating Function (
M Esakki Dharani, A Nagarajan, K Palani
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