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## Filters

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

1990
*
Discrete Mathematics
*

Thomason,

doi:10.1016/0012-365x(90)90365-o
fatcat:sxxbum4fhbc2fmftak75jckurq
*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. ...##
###
Bibliography on Domination in Graphs and Some Basic Definitions of Domination Parameters
[chapter]

1991
*
Annals of Discrete Mathematics
*

Thomason,

doi:10.1016/s0167-5060(08)71054-9
fatcat:ez3slvi5zbdy3iyvoez4ain4ey
*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. ...##
###
Introduction

1993
*
Discrete Applied Mathematics
*

A notion related

doi:10.1016/0166-218x(93)90217-c
fatcat:iklvodekpnho3nyhvmz6acnvuy
*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. ...##
###
Chordal Graphs and Upper Irredundance, Upper Domination and Independence
[chapter]

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. ...

##
###
Chordal graphs and upper irredundance, upper domination and independence

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. ...

##
###
Introduction

1990
*
Discrete Mathematics
*

Acknowledgements There can be little doubt that this special issue really has many editors; many people have

doi:10.1016/0012-365x(90)90343-g
fatcat:bu7spobm4nb4bpkraijn6knfue
*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 ...##
###
The complexity of irredundant sets parameterized by size

2000
*
Discrete Applied Mathematics
*

An

doi:10.1016/s0166-218x(99)00185-7
fatcat:knl4uvlvuvbrjbllvxhdk5o54m
*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. ...##
###
Breaking the 2n-barrier for Irredundance: Two lines of attack

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. ...

##
###
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

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. ...

##
###
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]

2020
*
arXiv
*
pre-print

It can be reduced

arXiv:2004.07214v1
fatcat:5atat6z2hrbzxci2iv7kbumrfa
*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, ). ...##
###
A Parameterized Route to Exact Puzzles: Breaking the 2 n -Barrier for Irredundance
[chapter]

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. ...

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

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. ...

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