Toughness and Maximum Extension of Certain \(t\)-Tough Sets of the Bloom Graph \(B_{m,n}\), \(m\ge 3\), \(n\ge 3\)

Authors

DOI:

https://doi.org/10.26713/cma.v12i4.1639

Keywords:

Toughness, Bloom Graph, Maximum Extension

Abstract

Data broadcasting is the process of distributing data sets from one or more nodes to other nodes in the network. The fault tolerance of the data broadcasting network plays key importance in its efficient performance. The toughness of graphs is a measure for the fault tolerance of a graph.  In this paper, we investigate the toughness and maximum extension of certain $t$-tough sets of the bloom graph \(B_{m,n}\), \(m\ge 3\), \(n\ge 3\).

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References

D. Bauer, S. L. Hakimi and E. Schmeichel, Recognizing tough graphs is NP-hard, Discrete Applied Mathematics 28 (1990), 191 – 195, DOI: 10.1016/0166-218X(90)90001-S.

D. Bauer, H. Broersma and E. Schmeichel, Toughness in graphs — A survey, Graphs and Combinatorics 22 (2006), 1 – 35, DOI: 10.1007/s00373-006-0649-0.

A. E. Brouwer, Toughness and spectrum of a graph, Linear Algebra and its Applications 226-228 (1995), 267–271, DOI: 10.1016/0024-3795(95)00154-J.

V. Chvátal, Tough graphs and Hamilton circuits, Discrete Mathematics 306(10-11) (2006), 910 – 917, DOI: 10.1016/j.disc.2006.03.011.

V.J. A. Cynthia and N. R. Swathi, A study on the toughness of certain graphs, Journal of Computer and Mathematical Sciences 8(11) (2017), 600 – 605, DOI: 10.29055/jcms/698.

V. J. A. Cynthia and N. R. Swathi, On the extension of a t-tough set of a graph, Mathematical Sciences International Research Journal 7 (2018), 48 – 52, URL: https://www.imrfjournals.com/msirj7s2.

K. K. Ferland and M. L. Holben, The tough sets of the generalised Petersen graphs G(n,2), Australian Journal of Combinatorics 34 (2006), 211 – 228, URL: https://ajc.maths.uq.edu.au/pdf/34/ajc_v34_p211.pdf.

W. D. Goddard and H. C. Swart, On the toughness of a graph, Quaestiones Mathematicae 13 (1990), 217 – 232, DOI: 10.1080/16073606.1990.9631613.

W. Goddard, M. D. Plummer and H. C. Swart, Maximum and minimum toughness of graphs with small genus, Discrete Mathematics 167-168 (1997), 329 – 339, DOI: 10.1016/S0012-365X(96)00238-5.

W. Goddard, The toughness of cubic graphs, Graphs and Combinatorics 12 (1996), 17 – 22, DOI: 10.1007/BF01858441.

X. Gu, Toughness in pseudo-random graphs, European Journal of Combinatorics 92 (2021), article number 103255, DOI: 10.1016/j.ejc.2020.103255.

D. Kratsch, J. Lehel and H. Müller, Toughness, Hamiltonicity and split graphs, Discrete Mathematics 150 (1996), 231 – 245, DOI: 10.1016/0012-365X(95)00190-8.

M. D. Plummer, Toughness and matching extensions in graphs, Discrete Mathematics 72 (1988), 311 – 320, DOI: 10.1016/0012-365X(88)90221-X.

G. J. Woeginger, The toughness of split graphs, Discrete Mathematics 190 (1998), 295 – 297, DOI: 10.1016/S0012-365X(98)00156-3.

D. A. Xavier, M. Rosary, E. Thomas and A. Arockiaraj, Broadcasting in bloom graph, International Journal of Mathematics and Soft Computing 6 (2016), 57 – 64, DOI: 10.26708/IJMSC.2016.2.6.06.

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Published

13-12-2021
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How to Cite

Swathi, N. R., & Cynthia, V. J. A. (2021). Toughness and Maximum Extension of Certain \(t\)-Tough Sets of the Bloom Graph \(B_{m,n}\), \(m\ge 3\), \(n\ge 3\). Communications in Mathematics and Applications, 12(4), 879–902. https://doi.org/10.26713/cma.v12i4.1639

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Research Article