Results 11 to 20 of about 11,106,432 (291)
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 Total Outer k-Independent Domination Number of Graphs
Mathematics, 2020 A set of vertices of a graph G is a total dominating set if every vertex of G is adjacent to at least one vertex in such a set. We say that a total dominating set D is a total outer k-independent dominating set of G if the maximum degree of the subgraph ...
Abel Cabrera-Martínez +3 more
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On domination and independent domination numbers of a graph [PDF]
Discrete Mathematics, 1978 AbstractFor a graph G, the definitions of domination number, denoted γ(G), and independent domination number, denoted i(G), are given, and the following results are obtained:Theorem. If G does not have an induced subgraph isomorphic to K1,3, then γ(G) = i(G).Corollary 1. For any graph G, γ(L(G))=i(L(G)), where L(G) is the line graph of G. (This extends
Robert B. Allan, Renu C. Laskar
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The independent domination number of a random graph [PDF]
Discussiones Mathematicae Graph Theory, 2011 We prove a two-point concentration for the independent domination number of the random graph Gn,p provided p 2 ln(n) 64ln((lnn)=p). occurs asymptotically almost surely (a.a.s.) if P(Gn;p has property A) ! 1 as n ! 1 . See Bollobas (2) for notation and terminology. Weber (7) showed if p = 1=2 then a.a.s. (Gn;p) is either blog2 n − log2(log2 nlnn)c + 1
Lane H. Clark, Darin Johnson
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Extremal connected graphs for independent domination number [PDF]
Discrete Mathematics, 2004 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Brigham, Robert C. +2 more
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On independent domination number of regular graphs [PDF]
Discrete Mathematics, 1999 A subset \(S\) of the vertex set of a graph \(G\) is called independent, if no two of its vertices are adjacent in \(G\). An independent set in \(G\) is maximal, if it is not a proper subset of another independent set of \(G\). The minimum number of vertices of a maximal independent set is the independent domination number \(i(G)\) of \(G\).
Peter Che Bor Lam +2 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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Isolate and independent domination number of some classes of graphs
AKCE International Journal of Graphs and Combinatorics, 2019 In this paper we compute isolate domination number and independent domination number of some well known classes of graphs. Also a counter example is provided, which disprove the result on independent domination for Euler Totient Cayley graph proved by ...
Shilpa T. Bhangale, Madhukar M. Pawar
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On trees with equal Roman domination and outer-independent Roman domination number [PDF]
Communications in Combinatorics and Optimization, 2019 A Roman dominating function (RDF) on a graph $G$ is a function $f : V (G) \to \{0, 1, 2\}$ satisfying the condition that every vertex $u$ for which $f(u) = 0$ is adjacent to at least one vertex $v$ for which $f(v) = 2$.
S. Nazari-Moghaddam, S.M. Sheikholeslami
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Independent Transversal Total Domination Versus Total Domination in Trees
Discussiones Mathematicae Graph Theory, 2021 A subset of vertices in a graph G is a total dominating set if every vertex in G is adjacent to at least one vertex in this subset. The total domination number of G is the minimum cardinality of any total dominating set in G and is denoted by γt(G).
Martínez Abel Cabrera +2 more
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