Filters








1,606 Hits in 5.5 sec

New results about the bondage number of a graph

Ulrich Teschner
1997 Discrete Mathematics  
The bondage number b(G) of a nonempty graph G was first introduced by Fink, Jacobson, Kinch and Roberts [3] . Among other results they showed that b(G)~<2 if G is a tree.  ...  In this paper we present a characterization of those trees having bondage number 1. Further on we present the first lower bounds for the bondage number and some new sharp upper bounds.  ...  Upper bounds for the bondage number From Proposition 2.6 we know that the bondage number of a graph G is bounded from above by A(G), when G is not vertex-critical.  ... 
doi:10.1016/s0012-365x(96)00007-6 fatcat:dem6fvbpszawzafsh2bw3rltnq

Application of Graph Theory in Transportation Networks

Sanjay kumar Bisen
2017 International Journal of Scientific Research and Management  
One of the possibilities when modelling a transport network is to use a graph with vertices and edges. They represent the nodes and arcs of such a network respectively.  ...  There are dozens of parameters or characteristics that we can describe in graphs, including the different types of domination number and the problems related to it.  ...  In this way, they introduced a new parameter called the bondage number of a graph.  ... 
doi:10.18535/ijsrm/v5i7.48 fatcat:5fi7r3yddjhxllsuwyg5kzbutu

On Bondage Numbers of Graphs: A Survey with Some Comments

Jun-Ming Xu
2013 International Journal of Combinatorics  
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 .  ...  The domination number of a graph is the smallest number of vertices which dominate all remaining vertices by edges of .  ...  the references [128] and [81] , which resulted in this version.  ... 
doi:10.1155/2013/595210 fatcat:6zg7jz7i5jenzc2e2izfdy2txq

Graph Theory Approach to the Vulnerability of Transportation Networks

Sambor Guze
2019 Algorithms  
The domination, edge-domination concepts, and related topics, such as bondage-connected and weighted bondage-connected numbers, were applied as the tools for searching and identifying the bottlenecks in  ...  Thus, many governments recognize it as a critical element in ensuring the daily existence of societies in their countries.  ...  In this way, they introduced the new parameter called the bondage number of a graph. It is defined in the following way.  ... 
doi:10.3390/a12120270 fatcat:qppy77jvmrarjilx3gxcwojody

BONDAGE AND STRONG-WEAK BONDAGE NUMBERS OF TRANSFORMATION GRAPHS $G^{xyz}$

A. Ayta{\c{c}}, T. Turaci
2016 International Journal of Pure and Applied Mathematics  
The bondage number b(G) of a nonempty graph G is the cardinality of a smallest set of edges whose removal from G results in a graph with domination number greater than γ(G).  ...  In this paper, the bondage parameters have been examined of transformation graphs, then exact values and upper bounds have been obtained.  ...  Acknowledgments This research was supported by "Faculty of Science, Ege University, Scientific Research Project: Code 2011/FEN/064".  ... 
doi:10.12732/ijpam.v106i2.30 fatcat:jjrkmaopt5gude2vb5smq2bx2m

On Bondage Numbers of Graphs -- a survey with some comments [article]

Jun-Ming Xu
2012 arXiv   pre-print
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.  ...  The exact value of bondage number for a general graph, there is a result as follows.  ... 
arXiv:1204.4010v1 fatcat:px2cuvbi6fhl5ci6hpoz5fyh3y

The bondage number of graphs:good and bad vertices

Vladimir Samodivkin
2008 Discussiones Mathematicae Graph Theory  
The bondage number b(G) of a nonempty graph G is the cardinality of a smallest set of edges whose removal from G results in a graph with domination number greater then γ(G).  ...  The domination number γ(G) of a graph G is the minimum number of vertices in a set D such that every vertex of the graph is either in D or is adjacent to a member of D.  ...  The bondage number b(G) of a nonempty graph G is the cardinality of a smallest set of edges whose removal from G results in a graph with domination number greater than γ(G).  ... 
doi:10.7151/dmgt.1419 fatcat:awczdvixwfejnkl47zg6ykna24

Page 7561 of Mathematical Reviews Vol. , Issue 98M [page]

1998 Mathematical Reviews  
Krishnamoorthy (1-RSP-C; Troy, NY ) 98m:05103 05C35 Teschner, Ulrich (D-AACH-M2; Aachen New results about the bondage number of a graph.  ...  The bondage number, 6(G), of a non-empty graph is the cardinality of the smallest subset of edges E for which y(G—E)>>(G). J. F. Fink et al.  ... 

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  ...  A related notion, by Fink, Jacobson, Kinch and Roberts in "The bondage number of a graph", is that of finding a set of edges F of smallest order (called the bondage number), whose removal increases the  ...  Almost as if by coincidence, it seems, we received the paper on "The discipline number of a graph" by Chvatal and Cook, soon after we had received the paper on "The bondage number of a graph" by Fink,  ... 
doi:10.1016/0012-365x(90)90343-g fatcat:bu7spobm4nb4bpkraijn6knfue

Page 2985 of Mathematical Reviews Vol. , Issue 99e [page]

1999 Mathematical Reviews  
The negative split bondage number b; (G) of G is the minimum cardinality among all sets of edges XY C E such that 7,(G — X) < y,(G) and the split bondage number b,(G) of G is the minimum cardinality among  ...  Let a(n,m,k) be the largest real number oa € [0,1] such that every graph of order n, with independence number at most m, contains a subgraph of order & and density at least ¢.  ... 

A Survey on the Effect of Graph Operations on the Domination Number of a Graph

Yamuna M, Karthika K
2016 International Journal of Engineering and Technology  
In this paper we present a brief survey on the impact of different kinds of graph operation on the domination number of a graph.  ...  The domination number of G, denoted by  ( G ), is the minimum cardinality of a dominating set. Different kinds of graph operations have different outcomes on the domination number of a graph.  ...  Some principle results of bondage number for trees plays an important role in the study of bondage number. Here we present some results. 2) Bondage Number for Trees: D.  ... 
doi:10.21817/ijet/2016/v8i6/160806234 fatcat:2yofovffhvcirkdywhnx52v76u

On the dominated chromatic number of certain graphs [article]

Saeid Alikhani, Mohammad R. Piri
2019 arXiv   pre-print
In this paper, we study the dominated chromatic number, dominated stability and dominated bondage number of certain graphs.  ...  Let G be a simple graph. The dominated coloring of G is a proper coloring of G such that each color class is dominated by at least one vertex.  ...  We need the following results to obtain results about dom-chromatic number of circulant graphs. (ii) Let G be a graph without isolated vertices. Then χ dom (G) ≤ χ(G).γ(G).  ... 
arXiv:1910.02685v1 fatcat:obfa4r7635f2tafuo23itveexi

An improved upper bound for the bondage number of graphs on surfaces [article]

Jia Huang
2012 arXiv   pre-print
The bondage number b(G) of a graph G is the smallest number of edges whose removal from G results in a graph with larger domination number.  ...  Our proof is based on the technique developed by Carlson-Develin and Gagarin-Zverovich, and includes some elementary calculus as a new ingredient.  ...  The bondage number b(G) of a graph G is defined as the smallest number of edges whose removal from G results in a graph with larger domination number.  ... 
arXiv:1111.5629v3 fatcat:5ohnymhxfvbofep2fvl7rjhcxi

Page 4558 of Mathematical Reviews Vol. , Issue 96h [page]

1996 Mathematical Reviews  
We prove a number of basic results about this new parameter, including several relating it to other parameters of a graph, operations on a graph, and Hamiltonian properties.”  ...  The strong bondage number b, for a graph G is the cardinality of the smallest number of edges F c E(G) such that y,(G — F) > y,(G).  ... 

Edge Cover Domination in Mangoldt Graph

L Madhavi, B Maheswari
2011 Momona Ethiopian Journal of Science  
In this paper the edge cover, edge domination set, bondage number, non -bondage number and their parameters have been obtained for these graphs. way a subset of the edge E of G with minimum cordinality  ...  In their recent study of arithmetic graphs associated with certain arithmetic functions, the authors have introduced a new class of arithmetic graphs associated with Mangoldt function Λ(n), n ≥ 1, an integer  ...  ACKNOWLEDGEMENTS The authors express their thanks to the referees for their critical suggestions which improved the clarity and cohesiveness of the paper.  ... 
doi:10.4314/mejs.v3i1.63683 fatcat:jzoudy6zy5fhljqldry3t6ocrq
« Previous Showing results 1 — 15 out of 1,606 results