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Bibliography on domination in graphs and some basic definitions of domination parameters

S.T. Hedetniemi, R.C. Laskar
1990 Discrete Mathematics  
Thomason, Contributions to the theory of domination, independence and irredundance in graphs, Discrete Math. 33 (1981) 249-258. E.J. Cockayne, B. Gamble and B.  ...  Thomason, Contributions to the theory of domination, independence and irredundance in graphs, Tech. Rept. DM-175-IR, Dept. Mathematics, Univ. Victoria, April 1979. C.J. Colbourn, J.M.  ... 
doi:10.1016/0012-365x(90)90365-o fatcat:sxxbum4fhbc2fmftak75jckurq

Bibliography on Domination in Graphs and Some Basic Definitions of Domination Parameters [chapter]

S.T. Hedetniemi, R.C. Laskar
1991 Annals of Discrete Mathematics  
Thomason, Contributions to the theory of domination, independence and irredundance in graphs, Discrete Math. 33 (1981) 249-258. E.J. Cockayne, B. Gamble and B.  ...  Thomason, Contributions to the theory of domination, independence and irredundance in graphs, Tech. Rept. DM-175-IR, Dept. Mathematics, Univ. Victoria, April 1979. C.J. Colbourn, J.M.  ... 
doi:10.1016/s0167-5060(08)71054-9 fatcat:ez3slvi5zbdy3iyvoez4ain4ey

Introduction

MartinCharles Golumbic, Renu Laskar
1993 Discrete Applied Mathematics  
A notion related to domination is that of irredundancy in graphs.  ...  It is known that for chordal graphs, the size of a largest minimal dominating set, the size of a maximum independent set, and the size of a maximum irredundant set are all equal.  ... 
doi:10.1016/0166-218x(93)90217-c fatcat:iklvodekpnho3nyhvmz6acnvuy

Chordal Graphs and Upper Irredundance, Upper Domination and Independence [chapter]

Michael S. Jacobson, Ken Peters
1991 Annals of Discrete Mathematics  
of the largest minimal dominating set and /3(G), the independence number, which is the order of the largest maximal independent set.  ...  In this paper we consider the following parameters: IR(G), the upper irredundance number, which is the order of the largest maximal irredundant set, I'(G), the upper domination number, which is the order  ...  Payan and A. Thomason, Contributions to the theory of domination, independence and irredundance in graphs, Discrete Math. 33 (3) (1981) 249-258.  ... 
doi:10.1016/s0167-5060(08)71038-0 fatcat:xprrhndbbjh3deitn4whpx6kka

Chordal graphs and upper irredundance, upper domination and independence

Michael S. Jacobson, Ken Peters
1990 Discrete Mathematics  
of the largest minimal dominating set and /3(G), the independence number, which is the order of the largest maximal independent set.  ...  In this paper we consider the following parameters: IR(G), the upper irredundance number, which is the order of the largest maximal irredundant set, I'(G), the upper domination number, which is the order  ...  Payan and A. Thomason, Contributions to the theory of domination, independence and irredundance in graphs, Discrete Math. 33 (3) (1981) 249-258.  ... 
doi:10.1016/0012-365x(90)90349-m fatcat:vko2dhf7ojebpdlul4l64qgtcy

Introduction

S.T. Hedetniemi, R.C. Laskar
1990 Discrete Mathematics  
Acknowledgements There can be little doubt that this special issue really has many editors; many people have contributed their time and energy to produce this collection of papers and have in the process  ...  David Sumner was one of the early researchers in domination theory and was perhaps the first one to consider the question of domination critical graphs.  ...  The present paper "Chordal graphs and upper irredundance, upper domination and independence" by Jacobson and Peters expands considerably upon this by presenting several other classes of graphs for which  ... 
doi:10.1016/0012-365x(90)90343-g fatcat:bu7spobm4nb4bpkraijn6knfue

The complexity of irredundant sets parameterized by size

Rodney G. Downey, Michael R. Fellows, Venkatesh Raman
2000 Discrete Applied Mathematics  
An irredundant set of vertices V ⊆ V in a graph G = (V; E) has the property that for ev- .  ...  Complexity classiÿcation of vertex set problems in this framework has proved to be both more interesting and more di cult.  ...  Acknowledgements We would like to thank Patricia Evans for the suggestion of having a look at the complexity of the dual problem, and S.  ... 
doi:10.1016/s0166-218x(99)00185-7 fatcat:knl4uvlvuvbrjbllvxhdk5o54m

Breaking the 2n-barrier for Irredundance: Two lines of attack

Daniel Binkele-Raible, Ljiljana Brankovic, Marek Cygan, Henning Fernau, Joachim Kneis, Dieter Kratsch, Alexander Langer, Mathieu Liedloff, Marcin Pilipczuk, Peter Rossmanith, Jakub Onufry Wojtaszczyk
2011 Journal of Discrete Algorithms  
The lower and the upper irredundance numbers of a graph G, denoted ir(G) and IR(G), respectively, are conceptually linked to the domination and independence numbers and have numerous relations to other  ...  The main contributions of this article are exact exponential-time algorithms breaking the 2 n -barrier for irredundance.  ...  In graph theory, the irredundance numbers have been extensively studied due to their relation to numerous other graph parameters.  ... 
doi:10.1016/j.jda.2011.03.002 fatcat:txstt3rsnbbcdppraf4sqyxm6q

Page 4664 of Mathematical Reviews Vol. , Issue 80M [page]

1980 Mathematical Reviews  
The parameter ir(G) [IR(G)], ¥(G) [T(G)] and i(G) [ Bo(G)] are defined to be the | smallest [largest] orders of maximal irredundant, minimal dominating and maximal independent sets of vertices of G, respec  ...  It is to such equations that this paper is de voted. We intend this as an introduction, and there is little in the way of original contribution.  ... 

Page 492 of Mathematical Reviews Vol. , Issue 82b [page]

1982 Mathematical Reviews  
Contributions to the theory of domination, independence and irredundance in graphs. Discrete Math. 33 (1981), no. 3, 249-258.  ...  The domination number and upper domination num- ber are, respectively, the minimum and maximum cardinalities taken over all minimal dominating sets of the graph. The independent 82b:05081  ... 

A Study on Domination in Vague Incidence Graph and Its Application in Medical Sciences

Yongsheng Rao, Saeed Kosari, Zehui Shao, Ruiqi Cai, Liu Xinyue
2020 Symmetry  
In particular, we discuss the well-known problems of vague incidence dominating set, valid degree, isolated vertex, vague incidence irredundant set and their cardinalities related to the dominating, etc  ...  They have also been employed in document summarization, and in secure systems designs for electrical grids; consequently, in this paper, we extend the concept of the FIG to the VIG, and show some of its  ...  All authors have read and agreed to the possible publication of the manuscript. Conflicts of Interest: The authors declare no conflict of interest.  ... 
doi:10.3390/sym12111885 fatcat:lnk6v7u2mvcftorjoggweoigaq

Page 5190 of Mathematical Reviews Vol. , Issue 99h [page]

1999 Mathematical Reviews  
In this paper, the authors establish interpolating theorems for various graph-theoretic parameters connected with independence, domination and irredundance.  ...  99h:05068 05 The paper contributes to the research concerning the size of the largest subtree with bounded maximum degree in a graph, initiated by S. Win [Abh. Math. Sem. Univ.  ... 

Enumerating minimal dominating sets in the (in)comparability graphs of bounded dimension posets [article]

Marthe Bonamy, Oscar Defrain, Piotr Micek, Lhouari Nourine
2020 arXiv   pre-print
It can be reduced to enumerating minimal dominating sets in a graph, in fact even to enumerating minimal dominating sets in an incomparability graph.  ...  Since the flipping method is a key tool for the best known algorithms enumerating minimal dominating sets in a number of graph classes, this yields direct improvements on the state of the art.  ...  We now de ne notations from order theory that will be used in the context of a poset and its comparability graph only. Let G be the comparability graph of a poset P = (V, ).  ... 
arXiv:2004.07214v1 fatcat:5atat6z2hrbzxci2iv7kbumrfa

A Parameterized Route to Exact Puzzles: Breaking the 2 n -Barrier for Irredundance [chapter]

Daniel Binkele-Raible, Ljiljana Brankovic, Henning Fernau, Joachim Kneis, Dieter Kratsch, Alexander Langer, Mathieu Liedloff, Peter Rossmanith
2010 Lecture Notes in Computer Science  
The lower and the upper irredundance numbers of a graph G, denoted ir(G) and IR(G) respectively, are conceptually linked to domination and independence numbers and have numerous relations to other graph  ...  Additionally, our work also appears to be the first example of a parameterized approach leading to a solution to a problem in exponential time algorithmics where the natural interpretation as an exact  ...  In graph theory, the irredundance numbers have been extensively studied due to their relation to numerous other graph parameters.  ... 
doi:10.1007/978-3-642-13073-1_28 fatcat:qxiifrdksfbqle7blmkdwd7yc4

Breaking the 2^n-Barrier for Irredundance: A Parameterized Route to Solving Exact Puzzles [article]

Ljiljana Brankovic, Henning Fernau, Joachim Kneis, Dieter Kratsch Alexander Langer Mathieu Liedloff Daniel Raible Peter Rossmanith
2009 arXiv   pre-print
The lower and the upper irredundance numbers of a graph G, denoted ir(G) and IR(G) respectively, are conceptually linked to domination and independence numbers and have numerous relations to other graph  ...  Additionally, our work also appears to be the first example of a parameterized approach leading to a solution to a problem in exponential time algorithmics where the natural interpretation as an exact  ...  In graph theory, the irredundance numbers have been extensively studied due to their relation to numerous other graph parameters.  ... 
arXiv:0909.4224v1 fatcat:bvjx4me43zgt5ddhvc7bsaqwcq
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