A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is `application/pdf`

.

## Filters

##
###
Algorithm and Hardness Results for Outer-connected Dominating Set in Graphs
[chapter]

2014
*
Lecture Notes in Computer Science
*

We show that the

doi:10.1007/978-3-319-04657-0_16
fatcat:msjgdy6xbvdtreibl6krj25lai
*Outer*-*connected**Domination*Decision*problem*can be solved*in*linear-time for*graphs**of*bounded tree-width. ... The Minimum*Outer*-*connected**Domination**problem*is to find an*outer*-*connected**dominating*set*of*minimum cardinality*of*the input*graph*G. ... . ✷*Complexity*difference*in**domination*and outerconnected*domination*Though*outer*-*connected**domination*is a variation*of**domination*, the*problems*differ*in**complexity*; that is, there are*graph*classes ...##
###
Algorithm and Hardness Results for Outer-connected Dominating Set in Graphs

2014
*
Journal of Graph Algorithms and Applications
*

We show that the

doi:10.7155/jgaa.00334
fatcat:54jx4ygd5jfurjrprdzeg5gb5u
*Outer*-*connected**Domination*Decision*problem*can be solved*in*linear-time for*graphs**of*bounded tree-width. ... The Minimum*Outer*-*connected**Domination**problem*is to find an*outer*-*connected**dominating*set*of*minimum cardinality*of*the input*graph*G. ... . ✷*Complexity*difference*in**domination*and outerconnected*domination*Though*outer*-*connected**domination*is a variation*of**domination*, the*problems*differ*in**complexity*; that is, there are*graph*classes ...##
###
On the complexity of the outer-connected bondage and the outer-connected reinforcement problems
[article]

2018
*
arXiv
*
pre-print

We define the

arXiv:1802.00649v1
fatcat:ac426ebh2vd23agfz2sr46lgte
*outer*-*connected*bondage number*of*a*graph*G as the minimum number*of*edges whose removal from G results*in*a*graph*with an*outer*-*connected**domination*number larger than the one for G. ... Also, the*outer*-*connected*reinforcement number*of*a*graph*G is defined as the minimum number*of*edges whose addition to G results*in*a*graph*with an*outer*-*connected**domination*number, which is smaller ... The*outer*-*connected**domination**problem*is shown to be an NP-complete*problem*for arbitrary*graphs**in*[3] . ...##
###
On the Total Outer k-Independent Domination Number of Graphs

2020
*
Mathematics
*

*In*addition, we give several Nordhaus–Gaddum type results. Finally, we prove that computing the

*total*

*outer*k-independent

*domination*number

*of*a

*graph*G is an NP-hard

*problem*. ... A set

*of*vertices

*of*a

*graph*G is a

*total*

*dominating*set if every vertex

*of*G is adjacent to at least one vertex

*in*such a set. ... Conflicts

*of*Interest: The authors declare no conflict

*of*interest. ...

##
###
Enumeration of Enumeration Algorithms
[article]

2016
*
arXiv
*
pre-print

*In*this paper, we enumerate enumeration

*problems*and algorithms. This survey is under construction. If you know some results not

*in*this survey or there is anything wrong, please let me know. ... Reference [250] Enumeration

*of*all minimal

*dominating*sets

*in*a line

*graph*Input A line

*graph*G. Output All minimal

*dominating*sets

*in*G.

*Complexity*O(||G|| 5 N 6 )

*total*time. ... Reference [117] 2.12.5 Enumeration

*of*all minimal edge-

*dominating*sets

*in*a

*graph*Input A

*graph*G. Output All minimal edge-

*dominating*sets

*in*G.

*Complexity*O(||L(G)|| 5 N 6 )

*total*time. ...

##
###
Parameterized Domination in Circle Graphs
[chapter]

2012
*
Lecture Notes in Computer Science
*

To the best

doi:10.1007/978-3-642-34611-8_31
fatcat:ey5ccdolajgwdgstpejirr3l5e
*of*our knowledge, nothing was known about the parameterized*complexity**of*these*problems**in*circle*graphs*. ... SET,*CONNECTED*DOMINAT-ING SET,*TOTAL**DOMINATING*SET, and ACYCLIC*DOMINATING*SET are W [1]hard*in*circle*graphs*, parameterized by the size*of*the solution. • Whereas both*CONNECTED**DOMINATING*SET and ... Acknowledgements We would like to thank Sylvain Guillemot for stimulating discussions that motivated some*of*the research carried out*in*this paper, and to the anonymous referees for helpful suggestions ...##
###
Capacitated Domination: Constant Factor Approximations for Planar Graphs
[chapter]

2011
*
Lecture Notes in Computer Science
*

*In*this paper, we provide the first constant factor approximation for this

*problem*on planar

*graphs*, based on a new perspective on the hierarchical structure

*of*

*outer*-planar

*graphs*. ... We consider the capacitated

*domination*

*problem*, which models a service-requirement assigning scenario and which is also a generalization

*of*the

*dominating*set

*problem*. ... The author would like to thank the anonymous referees for their very helpful comments on the layout

*of*this work. ...

##
###
Parameterized Domination in Circle Graphs

2013
*
Theory of Computing Systems
*

To the best

doi:10.1007/s00224-013-9478-8
fatcat:pwlbhdfkajfgba77xoncz7jhp4
*of*our knowledge, nothing was known about the parameterized*complexity**of*these*problems**in*circle*graphs*. ... SET,*CONNECTED*DOMINAT-ING SET,*TOTAL**DOMINATING*SET, and ACYCLIC*DOMINATING*SET are W [1]hard*in*circle*graphs*, parameterized by the size*of*the solution. • Whereas both*CONNECTED**DOMINATING*SET and ... Acknowledgements We would like to thank Sylvain Guillemot for stimulating discussions that motivated some*of*the research carried out*in*this paper, and to the anonymous referees for helpful suggestions ...##
###
Relating the total domination number and the annihilation number of cactus graphs and block graphs

2018
*
Ars Mathematica Contemporanea
*

The

doi:10.26493/1855-3974.1378.11d
fatcat:vrnib4npzncu7hllekqsygwete
*total**domination*number γ t (G)*of*a*graph*G is the order*of*a smallest set D ⊆ V (G) such that each vertex*of*G is adjacent to some vertex*in*D. ... It is conjectured that γ t (G) ≤ a(G) + 1 holds for every nontrivial*connected**graph*G. ... Similarly as*in*the proof for cactus*graphs*, all*outer**complex*cliques*in*the figures will be drawn with an exit-vertex x even though a unique*complex*clique*in*a block*graph*does not have one. ...##
###
Parameterized Domination in Circle Graphs
[article]

2012
*
arXiv
*
pre-print

To the best

arXiv:1205.3728v1
fatcat:oetngp7cqvcy3p2jphgc3gvufu
*of*our knowledge, nothing was known about the parameterized*complexity**of*these*problems**in*circle*graphs*. ... Keil [Discrete Applied Mathematics, 42(1):51-63, 1993] proved that*Dominating*Set,*Connected**Dominating*Set, and*Total**Dominating*Set are NP-complete*in*circle*graphs*. ... We would like to thank Sylvain Guillemot for stimulating discussions that motivated some*of*the research carried out*in*this paper. ...##
###
Outer-Convex Dominating Set in the Corona of Graphs as Encryption Key Generator

2020
*
Complexity
*

The proposed encryption utilizes the properties

doi:10.1155/2020/8316454
fatcat:dmf63yni75fl5acsmhrx6sq76a
*of**outer*-convex*dominating*set*in*the corona*of**graphs*to generate random keys from the shared keyword to every character*of*the message. ...*In*this paper, we present a new type*of*symmetric encryption by converting the classical monoalphabetic affine cipher into a polyalphabetic cipher. ... Let G be a*connected**graph**of*order m ≥ 2 and H be any*graph**of*order n. e set S ⊂ V(G ∘ H) is a minimum*outer*-convex*dominating*set*in*G ∘ H if 2*Complexity*S � ∪ x∈V(G) S x , where S x ⊆V(H x ) is a ...##
###
Cooperative mobile guards in grids

2007
*
Computational geometry
*

A grid P is a

doi:10.1016/j.comgeo.2006.11.002
fatcat:rzkgaisi7ngglcu4bmue43p3lq
*connected*union*of*vertical and horizontal segments. ...*In*this paper we discuss the classes*of*polygon-bounded grids and simple grids for which we propose a quadratic time algorithm for solving the*problem**of*finding the minimum weakly cooperative guard set ... There exists a solution*of*the 3DM*problem**in**graph*G(V ∪ M, E) iff there exists a*total**domination*set*of*cardinality q + 8|M|*in**graph*G * (V * , E * ). ...##
###
On three outer-independent domination related parameters in graphs
[article]

2018
*
arXiv
*
pre-print

*In*this paper, the 2-

*outer*-independent, the

*total*

*outer*-independent and the double

*outer*-independent

*domination*numbers

*of*

*graphs*are investigated. ... The double,

*total*or 2-

*outer*-independent

*domination*number

*of*G is the smallest possible cardinality

*of*any double,

*total*or 2-

*outer*-independent

*dominating*set

*of*G, respectively. ... That is, a

*total*

*dominating*set S

*in*G is said to be a

*total*

*outer*-independent

*dominating*set (TOID set) if V (G) \ S is independent. ...

##
###
FO and MSO approach to Some Graph Problems: Approximation and Poly time Results
[article]

2017
*
arXiv
*
pre-print

*In*particular, we show the existance

*of*linear-time algorithms on bounded tree-width

*graphs*for star coloring, cd-coloring, rainbow coloring, equitable coloring,

*total*

*dominating*set,

*connected*

*dominating*... Secondly, we present a monadic second order (MSO) logic to minimum

*graph*modification

*problems*, minimum

*dominating*set

*problem*and minimum coloring

*problem*and their variants. ... Min

*Total*

*Outer*

*Connected*

*Dominating*Set if it satisfies the following property M

*in*T otal

*Outer*

*Connected*Dom(S) = (|S| ≤ k) ∧ T otal

*Outer*

*Connected*Dom(S) CYCLE

*DOMINATING*SET: For a

*graph*G = (V, ...

##
###
On the computational complexity of upper fractional domination

1990
*
Discrete Applied Mathematics
*

This paper studies a nondiscrete generalization

doi:10.1016/0166-218x(90)90065-k
fatcat:colnl4yxejewtj32bgtdvkix7e
*of*T(G), the maximum cardinality*of*a minimal*dominating*set*in*a*graph*G = (K:E). ...*In*this paper we show that: (1) Tf(G) is computable and is always a rational number; (2) the decision*problems*corresponding to the*problems**of*computing T(G) and Tf(G) are NP-complete; (3) for trees rf ... Thus, to*dominate*all the cotails, the*total*value*of*the function for each*outer*cone must be greater than or equal to 1. ...
« Previous

*Showing results 1 — 15 out of 41,836 results*