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Simultaneous stratification and domination in graphs with minimum degree two
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: MichaelA. Henning J.E. MaritzIn this paper we continue the study of stratification and domination in graphs explored by Chartrand et al. in [4]. We define an F-coloring of a graph to be a red-blue coloring of the vertices such that every blue vertex... -
A Transition from Total Domination in Graphs to Transversals in Hypergraphs
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: MichaelA. Henning Anders YeoA set S of vertices in a graph G without isolated vertices is a total dominating set of G if every vertex of G is adjacent to a vertex in S. The total domination number of G is the minimum... -
Upper total domination versus upper paired-domination
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Paul Dorbec MichaelA. Henning John McCoyLet G be a graph with no isolated vertices. A set S of vertices in G is a total dominating set of G if every vertex of G is adjacent to some vertex in S, while a paired-dominating set of... -
Equivalence domination in graphs
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: S. Arumugam --- Core Group Research Facility (CGRF), National Centre for Advanced Research in Discrete Mathematics (n-CARDMATH), India Mustapha Chellali --- LAMDA-RO Laboratory, Department of Mathematics, Algeria TeresaW. Haynes --- Department of Mathematics, USAFor a graph G = (V, E), a subset S ⊆ V (G) is an equivalence dominating set if for every vertex v ∈ V (G) \ S, there exist two vertices u, w ∈ S such that the subgraph... -
Vertex Covers and Secure Domination in Graphs
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: AlewynP. Burger MichaelA. Henning JanH. van VuurenLet G = (V,E) be a graph and let S ⊆ V. The set S is a dominating set of G if every vertex in V \ S is adjacent to some vertex in S. The set S is a... -
A Characterization of Graphs with Disjoint Dominating and Total Dominating Sets
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: MichaelA. Henning Justin SoutheyA dominating set of a graph is a set of vertices such that every vertex not in the set is adjacent to a vertex in the set, while a total dominating set of a graph is a set of vertices... -
The disjunctive domination number of a graph
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Wayne Goddard --- Department of Mathematical Sciences, USA Michael A. Henning --- Department of Mathematics, South Africa Charles A. McPillan --- Department of Mathematical Sciences, USAFor a positive integer b, we define a set S of vertices in a graph G as a b-disjunctive dominating set if every vertex not in S is adjacent to a vertex of S or has at least b vertices... -
A new lower bound on the total domination number of a graph
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Majid Hajian --- Shahrood University of Technology, Iran Michael A. Henning --- University of Johannesburg, South Africa Nader Jafari Rad --- Shahed University, IranA set S of vertices in a graph G is a total dominating set of G if every vertex in G is adjacent to some vertex in S. The total domination number, γt (G), is the minimum cardinality of a... -
Further results on the independent Roman domination number of graphs
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Abel Cabrera Martínez --- Universitat Rovira i Virgili, Spain Frank A. Hernández Mira --- Universidad Autónoma de Guerrero, MéxicoLet f : V (G) → {0, 1, 2} be a function on a graph G with vertex set V (G). Let Vi = {v ∈ V (G) : f (v) = i} for every i ∈ {0, 1, 2}... -
On total domination and minimum maximal matchings in graphs
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Selim Bahadır --- Ankara Yıldırım Beyazıt University, TurkeyA subset M of the edges of a graph G is a matching if no two edges in M are incident. A maximal matching is a matching that is not contained in a larger matching. A subset S of vertices... -
Double total domination in the generalized lexicographic product of graphs
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Abel Cabrera-Martínez --- Universidad de Córdoba, Spain Ismael Ríos Villamar --- Universidad Autónoma de Guerrero, Mexico Juan M. Rueda-Vázquez --- Universidad de Córdoba, Spain José M. Sigarreta Almira --- Universidad Autónoma de Guerrero, MexicoLet G be a graph of minimum degree at least two. A set D ⊆ V(G) is said to be a double total dominating set of G if |N (v) ∩ D| ≥ 2 for every vertex v ∈ V(G)... -
Distance dominator packing coloring of type II
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Jasmina Ferme --- University of Maribor, Slovenia Daša Mesarič Štesl --- University of Ljubljana, SloveniaIn 2021, we introduced one type of the generalization of dominator coloring via packing coloring and distance domination. In this paper, we present a second type of such generalization, namely distance dominator packing coloring of type II, defined as follows... -
Maker-Breaker domination game played on corona products of graphs
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Athira Divakaran --- Mar Athanasius College, India Tijo James --- Pavanatma College, India Sandi Klavžar --- University of Ljubljana, Slovenia Latha S. Nair --- Mar Athanasius College, IndiaIn the Maker-Breaker domination game, Dominator and Staller play on a graph G by taking turns in which each player selects a not yet played vertex of G. Dominator’s goal is to select all the vertices in a dominating set,... -
Conceptualising and revealing political resistance in Zimbabwe through (re)naming roads in Bulawayo
Item type: Journal Article • Journal: South African Journal of African Languages • Authors: Nkululeko Sibanda --- Rhodes University, South Africa Progress Dube --- University of South Africa, South AfricaThe Zimbabwe central government issued a directive in November 2019 and early 2020 gazetting three statutory instruments for changes to names of buildings and streets as a directive to all local authorities to comply. In February 2020, the Bulawayo City... -
Distance domination and linear-vizing constants
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Paul Horn --- University of Denver, USA Di Qin --- University of Denver, USAGeneralizing and strengthening a classical result of Vizing, Rautenbach proved a linear relationship between the domination number, the maximum degree, the number of vertices, and the number of edges for graphs with no isolated vertices. The sharpest version of this... -
Strong domination number of graphs from primary subgraphs
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Saeid Alikhani --- Yazd University, Iran Nima Ghanbari --- University of Bergen, Norway Michael A. Henning --- University of Johannesburg, South AfricaA set D of vertices is a strong dominating set in a graph G, if for every vertex x ∈ V (G) \ D there is a vertex y ∈ D with xy ∈ E(G) and deg(x) ≤ deg(y). The... -
On the {2}-domination number of rooted product graphs
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: A. Cabrera-Martínez --- Universidad de Córdoba, Spain A. Conchado Peiró --- Universitat Politècnica de València, Spain J.M. Rueda-Vázquez --- Universidad de Córdoba, SpainLet G be a nontrivial graph with vertex set V (G). A function f : V (G) → {0, 1, 2} is called a {2}-dominating function on G if ∑ u ∈NG [v] f(u) ≥ 2 for every v... -
A note of 2-rainbow edge domination numbers of graphs
Item type: Journal Article • Journal: Quaestiones Mathematicae • Authors: Yu Yang --- School of Mathematics and Statistics, Huaibei Normal University, China Cai-Xia Wang --- School of Mathematics and Statistics, Northwest Normal University, China Shou-Jun Xu --- School of Mathematics and Statistics, Gansu Key Laboratory of Applied Mathematics and Complex Systems, Lanzhou University, ChinaLet G be a graph with edge set E containing no isolated vertices. A 2-rainbow edge dominating function of G is a function f from E to the family of all subsets of {1, 2} such that for each edge...