Fractional Strong Matching Preclusion for DHcube
Abstract
Let be a set edges and be a set of edges and/or vertices of a graph , then (resp. ) is a fractional matching preclusion set (resp. fractional strong matching preclusion set) if (resp. ) contains no fractional perfect matching. The fractional matching preclusion number (resp. fractional strong matching preclusion number) of is the minimum size of fractional matching preclusion set (resp. fractional strong matching preclusion set) of . In this paper, we obtain the fractional matching preclusion number and fractional strong matching preclusion number of the DHcube for . In addition, all the optimal fractional matching preclusion sets and fractional strong matching preclusion sets of these graphs are categorized.
References
- 1. , Perfect matching preclusion, Congressus Numerantium 174 (2005) 185–192. Google Scholar
- 2. , Matching preclusion for some interconnection networks, Networks 50 (2007) 173–180. Crossref, ISI, Google Scholar
- 3. , Matching preclusion for alternating group graphs and their generalizations, Int. J. Found. Comp. Sci. 19 (2008) 1413–1437. Link, ISI, Google Scholar
- 4. , Conditional Matching preclusion sets, Inf. Sci. 179 (2009) 1092–1101. Crossref, ISI, Google Scholar
- 5. , Fractional matching preclusion for (n, k)-star graphs, Parall. Process. Lett. 28 (2018) 1850017. Link, ISI, Google Scholar
- 6. , Matching preclusion for balanced hypercubes, Theor. Comput. Sci. 465 (2012) 10–20. Crossref, ISI, Google Scholar
- 7. , A new class of interconnection networks based on the alternating group, Networks 23 (1993) 315–326. Crossref, ISI, Google Scholar
- 8. , Strong matching preclusion, Theor. Comput. Sci. 412 (2011) 6409–6419. Crossref, ISI, Google Scholar
- 9. , Fractional matching preclusion of graphs, J. Comb. Optim. 34 (2016) 522–533. Crossref, ISI, Google Scholar
- 10. , Fractional matching preclusion for (burnt) pancake graphs, International Symposium on Pervasive Systems, Algorithms and Networks,
2018 . Google Scholar - 11. , Computers and Intractability: A Guide to the Theory of NP-Completeness (United States of America, 1979). Google Scholar
- 12. , The NP-completeness column: An ongoing guide, J. Algorithms 9 (1982) 426–444. Crossref, ISI, Google Scholar
- 13. , DVcube: A novel compound architecture of disc-ring graph and hypercube-like graph, Theor. Comput. Sci. 498 (2013) 28–45. Crossref, ISI, Google Scholar
- 14. , A class of hypercube-like networks, in Proc. of the 5th IEEE Symposium on Parallel and Distributed Processing (SPDP),
1993 , pp. 800–803. Google Scholar - 15. , Fractional matching preclusion for arrangement graphs, Discrete Appl. Math. 270 (2019) 181–189. Crossref, ISI, Google Scholar
- 16. , The crossed cube architecture for parallel computing, IEEE Trans. Parallel Distrib. Syst. 3 (1992) 513–524. Crossref, ISI, Google Scholar
- 17. ,
The twisted cube , PARLE: Parallel Architectures and Languages Europe, Volume 1: Parallel Architectures (1987), pp. 152–159. Crossref, Google Scholar - 18. , A variation on the hypercube with lower diameter, IEEE Trans. Comput. 40 (1991) 1312–1316. Crossref, ISI, Google Scholar
- 19. , The Möbius cubes, IEEE Trans. Comput. 44 (1995) 647–659. Crossref, ISI, Google Scholar
- 20. , The Mcube: A symmetrical cube based network with twisted links, in Proc. of the 9th IEEE International Parallel Processing Symposium (IPPS),
1995 , pp. 11–16. Google Scholar - 21. , KCube: A novel architecture for interconnection networks, Inform. Process. Lett. 110 (2010) 821–825. Crossref, ISI, Google Scholar
- 22. , Hamiltonian properties of some compound networks, Discrete Appl. Math. 239 (2018) 174–182. Crossref, ISI, Google Scholar


