Edge subdivision and edge multisubdivision versus some domination related parameters in generalized corona graphs [PDF]
Opuscula Mathematica, 2016 Given a graph \(G=(V,E)\), the subdivision of an edge \(e=uv\in E(G)\) means the substitution of the edge \(e\) by a vertex \(x\) and the new edges \(ux\) and \(xv\).
Magda Dettlaff +2 more
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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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On graphs with equal domination and independent domination numbers
Discrete Mathematics, 1991 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jerzy Topp, Lutz Volkmann
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Graphs with equal Grundy domination and independence number
Discrete Optimization, 2023 The Grundy domination number, ${γ_{\rm gr}}(G)$, of a graph $G$ is the maximum length of a sequence $(v_1,v_2,\ldots, v_k)$ of vertices in $G$ such that for every $i\in \{2,\ldots, k\}$, the closed neighborhood $N[v_i]$ contains a vertex that does not belong to any closed neighborhood $N[v_j]$, where ...
Gábor Bacsó +3 more
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On the Number of k‐Dominating Independent Sets [PDF]
Journal of Graph Theory, 2016 AbstractWe study the existence and the number of k‐dominating independent sets in certain graph families. While the case namely the case of maximal independent sets—which is originated from Erdős and Moser—is widely investigated, much less is known in general.
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Independent Rainbow Domination Numbers of Generalized Petersen Graphs P(n,2) and P(n,3)
Mathematics, 2020 We obtain new results on independent 2- and 3-rainbow domination numbers of generalized Petersen graphs P ( n , k ) for certain values of n , k ∈ N . By suitably adjusting and applying a well established technique of tropical algebra (path
Boštjan Gabrovšek +2 more
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The total co-independent domination number of some graph operations [PDF]
, 2022 [EN] A set D of vertices of a graph G is a total dominating set if every vertex of G is adjacent to at least one vertex of D. The total dominating set D is called a total co-independent dominating set if the subgraph induced by V (G)- D is edgeless.
González Yero, Ismael +4 more
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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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On independent domination numbers of grid and toroidal grid directed graphs [PDF]
Communications in Combinatorics and Optimization, 2019 A subset $S$ of vertex set $V(D)$ is an independent dominating set of a digraph $D$ if $S$ is both an independent and a dominating set of $D$. The independent domination number $i(D)$ is the minimum cardinality of an independent dominating set of $D ...
R. Shaheen
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An improved upper bound on the independent double Roman domination number of trees
AKCE International Journal of Graphs and Combinatorics, 2022 For a graph [Formula: see text] an independent double Roman dominating function (IDRDF) is a function [Formula: see text] having the property that: (i) every vertex [Formula: see text] with f(v) = 0 has a neighbor u with f(u) = 3 or at least two ...
F. Nahani Pour +3 more
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