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Some Algorithmic Results on Restrained Domination in Graphs
[article]
2016
arXiv
pre-print
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Finally, we give a new improved upper bound on the restrained domination number, cardinality of a minimum restrained dominating set in terms of number of vertices and minimum degree of graph. ...
In addition, we also propose polynomial time algorithms to solve the Minimum Restrained Domination problem in cographs and chain graphs. ...
In Section 2, some pertinent definitions and some preliminary results are discussed. ...
arXiv:1606.02340v1
fatcat:lrg6szttbralxhuc2mi6aqsyka
NP-completeness and APX-completeness of restrained domination in graphs
2012
Theoretical Computer Science
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In this paper, we investigate the NP-completeness of the restrained domination problem in planar graphs and split graphs. ...
Let G = (V , E) be a simple graph. A vertex set S ⊆ V is a restrained dominating set if every vertex not in S is adjacent to a vertex in S and to a vertex in V − S. ...
Acknowledgments The first and the third authors are supported in part by the National Natural Science Foundation of China ...
doi:10.1016/j.tcs.2012.05.005
fatcat:ejl2wswvufd7xhdztundoushgu
Split Restrained Dominating Set of an Interval Graph using an Algorithm
2012
International Journal of Applied Information Systems
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There has been persistent in the Algorithmic aspects of interval graphs in past decades spurred much by their numerous application of an interval graphs corresponding to an interval family I. A set ...
The various applications of the theory of Restrained domination, the most often discussed is communication network. ...
This research was supported in part by B.Maheswari, Sri Padmavathi Women's University,Tirupati, Andhra Pradesh, Tirupati. ...
doi:10.5120/ijais12-450751
fatcat:viioqia72rbs3kqup3etpnagx4
On the complexity of the bondage and reinforcement problems
2012
Journal of Complexity
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The bondage (resp. total bondage) number of a nonempty graph G is the smallest number of edges whose removal from G results in a graph with larger domination (resp. total domination) number of G. ...
The reinforcement (resp. total reinforcement) number of G is the smallest number of edges whose addition to G results in a graph with smaller domination (resp. total domination) number. ...
Acknowledgments The authors thank the anonymous referees for their kind comments and helpful suggestions on the original manuscript, which resulted in this final version. ...
doi:10.1016/j.jco.2011.11.001
fatcat:5pm3h3dzivexrpfgh6fzxwokpa
Page 1555 of Mathematical Reviews Vol. , Issue 2002C
[page]
2002
Mathematical Reviews
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A set S C V isa restrained dominating set if every vertex not in S is adjacent to a vertex in
S and to a vertex in V — S. ...
The restrained domination number of
G, denoted by y,(G), is the minimum cardinality of a restrained dominating set of G. ...
On Bondage Numbers of Graphs: A Survey with Some Comments
2013
International Journal of Combinatorics
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The bondage number of a nonempty graph is the smallest number of edges whose removal from results in a graph with domination number greater than the domination number of . ...
This paper gives a survey on the bondage number, including known results, conjectures, problems, and some comments, also selectively summarizes other types of bondage numbers. ...
the references [128] and [81] , which resulted in this version. ...
doi:10.1155/2013/595210
fatcat:6zg7jz7i5jenzc2e2izfdy2txq
(1,j)-set problem in graphs
[article]
2014
arXiv
pre-print
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In this paper, we first obtain an upper bound on γ_(1,j) (G) using probabilistic methods, for bounded minimum and maximum degree graphs. ...
Finally, we design two algorithms for finding γ_(1,j) (G) of a tree and a split graph, for any fixed j, which answers an open question posed in [CHHM13]. ...
Using this result, they also showed that domination number is equal to restrained domination number. ...
arXiv:1410.3091v1
fatcat:47ow2xoapbgbjjle4nswjgcrqe
The restrained double Roman domination and graph operations
[article]
2021
arXiv
pre-print
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And then we study the impact of some graph operations, such as strong product, cardinal product and corona with a graph, on restrained double Roman domination number. ...
In this paper, we first prove that the problem of computing RDRD-number is NP-hard even for chordal graphs. ...
Strong ProductIn this section, we first present some bounds on the restrained double Roman domination number of strong product graphs, moreover we determine the exact values of restrained double Roman ...
arXiv:2111.04363v1
fatcat:h4x6a2sblrcx7h57o3x7guh6x4
A note on restrained domination in self-complementary graphs
2019
Discussiones Mathematicae Graph Theory
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The restrained domination number of a graph G is the minimum cardinality of a restrained dominating set of G. In this paper, we study restrained domination in self-complementary graphs. ...
In particular, we characterize the self-complementary graphs having equal domination and restrained domination numbers. ...
Acknowledgement Research of the 2nd and 3rd authors supported in part by the University of Johannesburg. ...
doi:10.7151/dmgt.2222
fatcat:t6m5juc2cjczpftblay4obmeoy
Complexity of Bondage and Reinforcement
[article]
2011
arXiv
pre-print
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The reinforcement number of G is the smallest number of edges whose addition to G results in a graph with smaller domination number. ...
The bondage (resp. total bondage) number of a nonempty graph G is the smallest number of edges whose removal from G results in a graph with larger domination (resp. total domination) number of G. ...
A survey of selected recent results on total domination in Henning [9] . ...
arXiv:1109.1657v1
fatcat:2nwepptkpnf7nddmw6aelmfu2q
Optimization Models for Efficient (t, r) Broadcast Domination in Graphs
2021
Symmetry
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Known to be NP-complete, domination number problems in graphs and networks arise in many real-life applications, ranging from the design of wireless sensor networks and biological networks to social networks ...
While some theoretical approaches have been addressed for small values of t,r in the literature; in this work, we propose an approach from an optimization point of view. ...
While a linear programming model has been applied to obtain some domination parameters, e.g., strong domination, restrained domination and strong restrained domination [6] , weighted total domination ...
doi:10.3390/sym13061028
fatcat:ouq32lajojcetjacry64c7lbsq
Restrained double Roman domination of a graph
[article]
2021
arXiv
pre-print
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Then we present an upper bound on the restrained double Roman domination number of a connected graph G in terms of the order of G and characterize the graphs attaining this bound. ...
The weight of a restrained double Roman dominating function f is the sum f(V)=∑_v∈Vf(v), and the minimum weight of a restrained double Roman dominating function on G is the restrained double Roman domination ...
RDRD number of some graphs In this section we investigate the exact value of the restrained double Roman domination number of some graphs. Observation 3. ...
arXiv:2106.08501v1
fatcat:bhrlqt4lzffmbdlr7tpjebwfeu
On Bondage Numbers of Graphs -- a survey with some comments
[article]
2012
arXiv
pre-print
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The bondage number of a nonempty graph G is the cardinality of a smallest edge set whose removal from G results in a graph with domination number greater than the domination number of G. ...
This lecture gives a survey on the bondage number, including the known results, problems and conjectures. We also summarize other types of bondage numbers. ...
In this section, we will state some results and problems on the bondage number for a planar graph. Recall some results on planar graphs used in this section. ...
arXiv:1204.4010v1
fatcat:px2cuvbi6fhl5ci6hpoz5fyh3y
γ-Excellent, critically dominated, end-dominated, and dot-critical trees are equivalent
2007
Discrete Mathematics
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A graph is -excellent if every vertex of the graph is contained in some minimum dominating set of the graph. A vertex v is critical in G if the domination number of G − v is smaller than that of G. ...
The graph G is dot-critical if contracting any edge of G produces a graph with smaller domination number. G is critically dominated if the set of critical vertices forms a dominating set for G. ...
Burton and Sumner [6] introduced the concept of a dot-critical graph as one in which identifying any two adjacent vertices (i.e., contracting the edge comprising those vertices) results in a graph with ...
doi:10.1016/j.disc.2006.02.016
fatcat:k7hkttq6pvegremd6wn4nlqpie
A note on trees, tables, and algorithms
2009
Networks
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Several algorithms for optimal vertex subsets in trees are given by simple tables. In this paper we investigate the properties of and operations on these tables. ...
We use known techniques for combining tables to correct a table in the literature; give a necessary and sufficient condition for a table to correspond to some tree property; discuss the question of dividing ...
Figure 3 : 3 The tables for restrained-ness and restrained domination. ...
doi:10.1002/net.20282
fatcat:z4oeob54b5dqxo6pg47lvv2bka
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