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

B. S. Panda, Arti Pandey
2014 Lecture Notes in Computer Science  
We show that the 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  ... 
doi:10.1007/978-3-319-04657-0_16 fatcat:msjgdy6xbvdtreibl6krj25lai

Algorithm and Hardness Results for Outer-connected Dominating Set in Graphs

B. S. Panda, Arti Pandey
2014 Journal of Graph Algorithms and Applications  
We show that the 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  ... 
doi:10.7155/jgaa.00334 fatcat:54jx4ygd5jfurjrprdzeg5gb5u

On the complexity of the outer-connected bondage and the outer-connected reinforcement problems [article]

M. Hashemipour, M. R. Hooshmandasl, A. Shakiba
2018 arXiv   pre-print
We define the 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] .  ... 
arXiv:1802.00649v1 fatcat:ac426ebh2vd23agfz2sr46lgte

On the Total Outer k-Independent Domination Number of Graphs

Abel Cabrera Martínez, J. C. Hernández-Gómez, E. Parra Inza, José M. Sigarreta
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.  ... 
doi:10.3390/math8020194 fatcat:rpplta7sjjfqpj7qxagagqxp4e

Enumeration of Enumeration Algorithms [article]

Kunihiro Wasa
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.  ... 
arXiv:1605.05102v2 fatcat:bwmhesagkje5hmynqyij7jv224

Parameterized Domination in Circle Graphs [chapter]

Nicolas Bousquet, Daniel Gonçalves, George B. Mertzios, Christophe Paul, Ignasi Sau, Stéphan Thomassé
2012 Lecture Notes in Computer Science  
To the best 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  ... 
doi:10.1007/978-3-642-34611-8_31 fatcat:ey5ccdolajgwdgstpejirr3l5e

Capacitated Domination: Constant Factor Approximations for Planar Graphs [chapter]

Mong-Jen Kao, D. T. Lee
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.  ... 
doi:10.1007/978-3-642-25591-5_51 fatcat:rq44gv2rtrcopezuy7ybx6av5i

Parameterized Domination in Circle Graphs

Nicolas Bousquet, Daniel Gonçalves, George B. Mertzios, Christophe Paul, Ignasi Sau, Stéphan Thomassé
2013 Theory of Computing Systems  
To the best 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  ... 
doi:10.1007/s00224-013-9478-8 fatcat:pwlbhdfkajfgba77xoncz7jhp4

Relating the total domination number and the annihilation number of cactus graphs and block graphs

Csilla Bujtás, Marko Jakovac
2018 Ars Mathematica Contemporanea  
The 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.  ... 
doi:10.26493/1855-3974.1378.11d fatcat:vrnib4npzncu7hllekqsygwete

Parameterized Domination in Circle Graphs [article]

Nicolas Bousquet, Daniel Gonçalves, George B. Mertzios, Christophe Paul, Ignasi Sau, Stéphan Thomassé
2012 arXiv   pre-print
To the best 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.  ... 
arXiv:1205.3728v1 fatcat:oetngp7cqvcy3p2jphgc3gvufu

Outer-Convex Dominating Set in the Corona of Graphs as Encryption Key Generator

Zehui Shao, S. Kosari, R. Anoos, S. M. Sheikholeslami, J. A. Dayap, Rosa M. Lopez Gutierrez
2020 Complexity  
The proposed encryption utilizes the properties 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  ... 
doi:10.1155/2020/8316454 fatcat:dmf63yni75fl5acsmhrx6sq76a

Cooperative mobile guards in grids

Adrian Kosowski, Michał Małafiejski, Paweł Żyliński
2007 Computational geometry  
A grid P is a 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 * ).  ... 
doi:10.1016/j.comgeo.2006.11.002 fatcat:rzkgaisi7ngglcu4bmue43p3lq

On three outer-independent domination related parameters in graphs [article]

Doost Ali Mojdeh, Iztok Peterin, Babak Samadi, Ismael G. Yero
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.  ... 
arXiv:1812.10946v1 fatcat:yjcrn2g5dbbzbm6ndfdora42tu

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

Kona Harshita, Sounaka Mishra, Renjith. P, N. Sadagopan
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,  ... 
arXiv:1711.02889v1 fatcat:neftvoxxhfeuhm4744zcjvwmgq

On the computational complexity of upper fractional domination

Grant A. Cheston, G. Fricke, S.T. Hedetniemi, D. Pokrass Jacobs
1990 Discrete Applied Mathematics  
This paper studies a nondiscrete generalization 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.  ... 
doi:10.1016/0166-218x(90)90065-k fatcat:colnl4yxejewtj32bgtdvkix7e
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