scholarly journals From the Quasi-Total Strong Differential to Quasi-Total Italian Domination in Graphs

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 1036
Author(s):  
Abel Cabrera Martínez ◽  
Alejandro Estrada-Moreno ◽  
Juan Alberto Rodríguez-Velázquez
Keyword(s):  
Vertex Cover ◽  
Domination Number ◽  
Theoretical Computer Science ◽  
Discrete Mathematics ◽  
Special Issue ◽  
Total Domination Number ◽  
Theoretical Computer ◽  
Graph Parameters ◽  
Semitotal Domination ◽  
Domination In Graphs

This paper is devoted to the study of the quasi-total strong differential of a graph, and it is a contribution to the Special Issue “Theoretical computer science and discrete mathematics” of Symmetry. Given a vertex x∈V(G) of a graph G, the neighbourhood of x is denoted by N(x). The neighbourhood of a set X⊆V(G) is defined to be N(X)=⋃x∈XN(x), while the external neighbourhood of X is defined to be Ne(X)=N(X)∖X. Now, for every set X⊆V(G) and every vertex x∈X, the external private neighbourhood of x with respect to X is defined as the set Pe(x,X)={y∈V(G)∖X:N(y)∩X={x}}. Let Xw={x∈X:Pe(x,X)≠⌀}. The strong differential of X is defined to be ∂s(X)=|Ne(X)|−|Xw|, while the quasi-total strong differential of G is defined to be ∂s*(G)=max{∂s(X):X⊆V(G)andXw⊆N(X)}. We show that the quasi-total strong differential is closely related to several graph parameters, including the domination number, the total domination number, the 2-domination number, the vertex cover number, the semitotal domination number, the strong differential, and the quasi-total Italian domination number. As a consequence of the study, we show that the problem of finding the quasi-total strong differential of a graph is NP-hard.

scholarly journals Foreword to the special issue dedicated to the tenth ''Journées montoises d'informatique théorique''

2007 ◽  
Vol Vol. 9 no. 2 ◽  
Author(s):  
Véronique Bruyère ◽  
Michel Rigo
Keyword(s):  
Computer Science ◽  
Coding Theory ◽  
Theoretical Computer Science ◽  
Discrete Mathematics ◽  
Combinatorics On Words ◽  
Special Issue ◽  
Theoretical Computer ◽  
Universitair Centrum ◽  
Numeration Systems ◽  
The University

Held at the Institute of Mathematics of the University of Liège, Liège, September 8―11, 2004 International audience This special issue of Discrete Mathematics & Theoretical Computer Science is dedicated to the tenth "Journées montoises d'informatique théorique" conference (Mons theoretical computer science days) which was held, for the first time, at the Institute of Mathematics of the University of Liège, Belgium, From 8th to 11th September 2004. Previous editions of this conference took place in Mons 1990, 1992, 1994, 1998, in Rouen 1991, in Bordeaux 1993, Marseille 1995, Marne-La-Vallée 2000 and Montpellier 2002.<p> This tenth edition can be considered as a widely international one. We were lucky to have almost 85 participants from fourteen different countries: Austria, Belgium, Burkina Faso, Canada, Czech republic, Finland, France, Germany, Israel, Italy, Japan, Norway, Poland and Portugal. The main proportion of researchers participating to this event was coming from France and Italy where a long tradition of combinatorics on words is well established. During four days, 42 contributed talks and 7 invited talks were given, the main topics being combinatorics on words, numeration systems, automata and formal languages theory, coding theory, verification, bio-informatics, number theory, grammars, text algorithms, symbolic dynamics and tilings. The invited speakers were: J. Cassaigne (CNRS, Luminy-Marseille), D. Caucal (IRISIA-CNRS, Rennes), C. Frougny (LIAFA, Université Paris 8), T. Helleseth (University of Bergen), S. Langerman (FNRS, Université Libre de Bruxelles), F. Neven (Limburgs Universitair Centrum, Diepenbeek), M.-F. Sagot (Inria Rhône-Alpes, Université Lyon I).<p> We would like to thanks all the participants, the invited speakers and the anonymous referees who made possible this event and special issue. Each paper has been refereed using high scientific standard by two independent referees. Readers of this special issue may wonder why it took so long to obtain it. We have encountered some problems with the formerly chosen journal and for the benefit of the contributors to this issue, we have chosen Discrete Mathematics & Theoretical Computer Science to publish their work.

scholarly journals $2\times 2$ monotone grid classes are finitely based

2016 ◽  
Vol Vol. 18 no. 2, Permutation... (Permutation Patterns) ◽  
Author(s):  
Michael Albert ◽  
Robert Brignall
Keyword(s):  
Computer Science ◽  
General Result ◽  
Theoretical Computer Science ◽  
Discrete Mathematics ◽  
Finite Collection ◽  
Permutation Patterns ◽  
Finitely Based ◽  
Special Issue ◽  
Theoretical Computer

In this note, we prove that all $2 \times 2$ monotone grid classes are finitely based, i.e., defined by a finite collection of minimal forbidden permutations. This follows from a slightly more general result about certain $2 \times 2$ (generalized) grid classes having two monotone cells in the same row. Comment: 10 pages, 5 figures. To appear in Discrete Mathematics and Theoretical Computer Science, special issue for Permutation Patterns 2015

scholarly journals On the Outer-Independent Roman Domination in Graphs

Symmetry ◽  
2020 ◽  
Vol 12 (11) ◽  
pp. 1846 ◽  
Author(s):  
Abel Cabrera Martínez ◽  
Suitberto Cabrera García ◽  
Andrés Carrión García ◽  
Angela María Grisales del Rio
Keyword(s):  
Minimum Weight ◽  
Domination Number ◽  
Independent Set ◽  
Theoretical Computer Science ◽  
Discrete Mathematics ◽  
Roman Domination ◽  
Roman Domination Number ◽  
Product Graphs ◽  
Isolated Vertex ◽  
Domination In Graphs

Let G be a graph with no isolated vertex and f:V(G)→{0,1,2} a function. Let Vi={v∈V(G):f(v)=i} for every i∈{0,1,2}. The function f is an outer-independent Roman dominating function on G if V0 is an independent set and every vertex in V0 is adjacent to at least one vertex in V2. The minimum weight ω(f)=∑v∈V(G)f(v) among all outer-independent Roman dominating functions f on G is the outer-independent Roman domination number of G. This paper is devoted to the study of the outer-independent Roman domination number of a graph, and it is a contribution to the special issue “Theoretical Computer Science and Discrete Mathematics” of Symmetry. In particular, we obtain new tight bounds for this parameter, and some of them improve some well-known results. We also provide closed formulas for the outer-independent Roman domination number of rooted product graphs.

scholarly journals Quadruple Roman Domination in Trees

Symmetry ◽  
2021 ◽  
Vol 13 (8) ◽  
pp. 1318
Author(s):  
Zheng Kou ◽  
Saeed Kosari ◽  
Guoliang Hao ◽  
Jafar Amjadi ◽  
Nesa Khalili
Keyword(s):  
Open Neighborhood ◽  
Minimum Weight ◽  
Domination Number ◽  
Theoretical Computer Science ◽  
Upper And Lower Bounds ◽  
Discrete Mathematics ◽  
Roman Domination ◽  
Roman Domination Number ◽  
Vertex Set ◽  
Roman Dominating Function

This paper is devoted to the study of the quadruple Roman domination in trees, and it is a contribution to the Special Issue “Theoretical computer science and discrete mathematics” of Symmetry. For any positive integer k, a [k]-Roman dominating function ([k]-RDF) of a simple graph G is a function from the vertex set V of G to the set {0,1,2,…,k+1} if for any vertex u∈V with f(u)<k, ∑x∈N(u)∪{u}f(x)≥|{x∈N(u):f(x)≥1}|+k, where N(u) is the open neighborhood of u. The weight of a [k]-RDF is the value Σv∈Vf(v). The minimum weight of a [k]-RDF is called the [k]-Roman domination number γ[kR](G) of G. In this paper, we establish sharp upper and lower bounds on γ[4R](T) for nontrivial trees T and characterize extremal trees.

The minus total k-domination numbers in graphs

2021 ◽  
pp. 2150150
Author(s):  
Jonecis Dayap ◽  
Nasrin Dehgardi ◽  
Leila Asgharsharghi ◽  
Seyed Mahmoud Sheikholeslami
Keyword(s):  
Domination Number ◽  
Total Domination ◽  
Total Domination Number ◽  
Sharp Bounds ◽  
Number Formula ◽  
Domination In Graphs ◽  
Dominating Function ◽  
Domination Numbers

For any integer [Formula: see text], a minus total [Formula: see text]-dominating function is a function [Formula: see text] satisfying [Formula: see text] for every [Formula: see text], where [Formula: see text]. The minimum of the values of [Formula: see text], taken over all minus total [Formula: see text]-dominating functions [Formula: see text], is called the minus total [Formula: see text]-domination number and is denoted by [Formula: see text]. In this paper, we initiate the study of minus total [Formula: see text]-domination in graphs, and we present different sharp bounds on [Formula: see text]. In addition, we determine the minus total [Formula: see text]-domination number of some classes of graphs. Some of our results are extensions of known properties of the minus total domination number [Formula: see text].

scholarly journals Introduction

2018 ◽  
Vol 27 (4) ◽  
pp. 441-441
Author(s):  
PAUL BALISTER ◽  
BÉLA BOLLOBÁS ◽  
IMRE LEADER ◽  
ROB MORRIS ◽  
OLIVER RIORDAN
Keyword(s):  
Computer Science ◽  
Theoretical Computer Science ◽  
Special Issue ◽  
Open Problems ◽  
Theoretical Computer ◽  
Discrete Probability ◽  
The Common

This special issue is devoted to papers from the meeting on Combinatorics and Probability, held at the Mathematisches Forschungsinstitut in Oberwolfach from the 17th to the 23rd April 2016. The lectures at this meeting focused on the common themes of Combinatorics and Discrete Probability, with many of the problems studied originating in Theoretical Computer Science. The lectures, many of which were given by young participants, stimulated fruitful discussions. The fact that the participants work in different and yet related topics, and the open problems session held during the meeting, encouraged interesting discussions and collaborations.

scholarly journals SPECIAL ISSUE ON MEMBRANE COMPUTING, Seventh Brainstorming Week on Membrane Computing

2009 ◽  
Vol 4 (3) ◽  
pp. 204
Author(s):  
Giancarlo Mauri ◽  
Gheorghe Păun ◽  
Agustín Riscos-Núñez
Keyword(s):  
Computer Science ◽  
Membrane Computing ◽  
Science Volume ◽  
Theoretical Computer Science ◽  
Natural Computing ◽  
Special Issue ◽  
Theoretical Computer ◽  
Generation Computing ◽  
New Generation ◽  
Selection Of

<p>The present volume contains a selection of papers resulting from the Seventh Brainstorming Week on Membrane Computing (BWMC7), held in Sevilla, from February 2 to February 6, 2009. The meeting was organized by the Research Group on Natural Computing (RGNC) from Department of Computer Science and Artificial Intelligence of Sevilla University. The previous editions of this series of meetings were organized in Tarragona (2003), and Sevilla (2004 – 2008). After the first BWMC, a special issue of Natural Computing – volume 2, number 3, 2003, and a special issue of New Generation Computing – volume 22, number 4, 2004, were published; papers from the second BWMC have appeared in a special issue of Journal of Universal Computer Science – volume 10, number 5, 2004, as well as in a special issue of Soft Computing – volume 9, number 5, 2005; a selection of papers written during the third BWMC has appeared in a special issue of International Journal of Foundations of Computer Science – volume 17, number 1, 2006); after the fourth BWMC a special issue of Theoretical Computer Science was edited – volume 372, numbers 2-3, 2007; after the fifth edition, a special issue of International Journal of Unconventional Computing was edited – volume 5, number 5, 2009; finally, a selection of papers elaborated during the sixth BWMC has appeared in a special issue of Fundamenta Informaticae</p>

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