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Graph Domination in Distance Two
Discussiones Mathematicae Graph Theory, 2005 A subgraph \(D\) of a graph \(G\) is \(k\)-dominating in \(G\) if every vertex of \(G-D\) is of distance \(\leq k\) from a vertex of \(D\). If \(\mathcal D\) is a specified class of graphs, Dom\(_k \mathcal D\) consists of all those graphs \(G\) in which every connected induced subgraph \(H\) has a \(k\)-dominating induced subgraph \(D \in {\mathcal D}\
Bacsó, Gábor +2 more
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Hop total Roman domination in graphs
AKCE International Journal of Graphs and Combinatorics, 2023 In this article, we initiate a study of hop total Roman domination defined as follows: a hop total Roman dominating function (HTRDF) on a graph [Formula: see text] is a function [Formula: see text] such that for every vertex u with f(u) = 0 there exists ...
H. Abdollahzadeh Ahangar +3 more
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Average distances and distance domination numbers
Discrete Applied Mathematics, 2009 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Tian, Fang, Xu, Jun-Ming
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Discussiones Mathematicae Graph Theory, 2021 In this paper, we study a new distance parameter triameter of a connected graph G, which is defined as max{d(u; v)+d(v;w)+d(u;w) : u; v;w ∈ V }and is denoted by tr(G).
Das Angsuman
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The Semitotal Domination Problem in Block Graphs
Discussiones Mathematicae Graph Theory, 2022 A set D of vertices in a graph G is a dominating set of G if every vertex outside D is adjacent in G to some vertex in D. A set D of vertices in G is a semitotal dominating set of G if D is a dominating set of G and every vertex in D is within distance 2
Henning Michael A. +2 more
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Distance domination-critical graphs
Applied Mathematics Letters, 2008 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Tian, Fang, Xu, Jun-Ming
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Unique Minimum Semipaired Dominating Sets in Trees
Discussiones Mathematicae Graph Theory, 2023 Let G be a graph with vertex set V. A subset S ⊆ V is a semipaired dominating set of G if every vertex in V \ S is adjacent to a vertex in S and S can be partitioned into two element subsets such that the vertices in each subset are at most distance two ...
Haynes Teresa W., Henning Michael A.
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Distance d-Domination Games [PDF]
, 2010 We study graph searching games where a number of cops try to capture a robber that is hiding in a system of tunnels modelled as a graph. While the current position of the robber is unknown to the cops, each cop can see a certain radius d around his position.
Stephan Kreutzer, Sebastian Ordyniak
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Zeroth-order general Randić index of trees with given distance k-domination number
Electronic Journal of Graph Theory and Applications, 2022 The zeroth-order general Randić index of a graph G is defined as Ra(G)=∑v ∈ V(G)dGa(v), where a ∈ ℝ, V(G) is the vertex set of G and dG(v) is the degree of a vertex v in G.
Tomas Vetrik +2 more
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The Numerical Invariants concerning the Total Domination for Generalized Petersen Graphs
Journal of Mathematics, 2020 A subset S of VG is called a total dominating set of a graph G if every vertex in VG is adjacent to a vertex in S. The total domination number of a graph G denoted by γtG is the minimum cardinality of a total dominating set in G.
Taiyin Zhao +4 more
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