Regular Connected Bipancyclic Spanning Subgraphs of Torus Networks
Abstract
It is well known that an -dimensional torus is Hamiltonian. Then the torus contains a spanning subgraph which is 2-regular and 2-connected. In this paper, we explore a strong property of torus networks. We prove that for any even integer with , the torus contains a spanning subgraph which is -regular, k-connected and bipancyclic; and if is odd, the result holds when some is even.
References
- 1. , Graph Theory with Applications (Springer, New York, 1980). Google Scholar
- 2. , On 4-regular 4-connected bipancyclic subgraph of hypercubes, Discrete Math. Algorithms Appl. 9 (2017). Link, Google Scholar
- 3. , Decomposition of hypercubes into regular connected bipancyclic subgraphs, Discrete Math. Algorithms Appl. 7 (2015). Link, Google Scholar
- 4. , Fault-tolerant bipancyclicity of faulty hypercubes under the generalized conditional-fault model, IEEE Trans. Comput. 59 (2011) 3400–3409. Google Scholar
- 5. , Panconnectivity and edge-pancyclicity of multidimensional torus, Discrete Appl. Math. 178 (2014) 33–45. Crossref, Google Scholar
- 6. , Distance preserving subgraphs of hypercubes, Journal of Combinatorial Theory, Series B 14 (1973) 263–267. Crossref, Google Scholar
- 7. , Leafy spanning trees in hypercubes, Appl. Math. Lett. 14 (2001) 801–804. Crossref, Google Scholar
- 8. , Fault-tolerant cycle embedding in the hypercube, Parallel Comput. 29 (2003) 821–832. Crossref, ISI, Google Scholar
- 9. , Some small sized spanning subgraphs of a hypercubes, Comput. Math. Appl. 34 (1997) 51–57. Crossref, Google Scholar
- 10. , Panconnectivity and edge-pancyclicity of k-ary n-cube, Networks 54 (2009) 1–11. Crossref, Google Scholar
- 11. , Spanning subgraphs of a hypercubes II: Double starlike trees, Math. Comput. Model. 11 (1988) 216–217. Crossref, Google Scholar
- 12. , Spanning subgraphs of a hypercubes IV: Rooted trees, Math. Comput. Model. 17 (1993) 85–88. Crossref, Google Scholar
- 13. , Edge-bipancyclicity of a hypercube with faulty vertices and edges, Discrete Appl. Math. 156 (2008) 1802–1808. Crossref, Google Scholar
- 14. , Spanning graphs of hypercubes: Starlike and double starlike trees, Discrete Math. 244 (2002) 231–239. Crossref, Google Scholar
- 15. , Note spanning tree congestion of the hypercube, Discrete Math. 309 (2009) 6644–6648. Crossref, ISI, Google Scholar
- 16. , Pancyclicity of k-ary n-cube networks with faulty vertices and edges, Discrete Appl. Math. 160 (2012) 231–238. Crossref, ISI, Google Scholar
- 17. , Edge-bipancyclicity of the k-ary n-cubes with faulty nodes and edges, Inform. Sci. 181 (2011) 2260–2267. Crossref, ISI, Google Scholar
- 18. , Embedding cycles and paths in product networks and their applications to multiprocessor systems, J. IEEE Trans. Parallel Distrib. Syst. 23 (2012) 1081–1089. Crossref, ISI, Google Scholar
- 19. , Panconnectivity and edge-pancyclicity of k-ary n-cubes with faulty elements, Discrete Appl. Math. 159 (2011) 212–223. Crossref, Google Scholar
- 20. , Regular connected bipancyclic spanning subgraphs of hypercubes, Comput. Math. Appl. 62 (2011) 3551–3554. Crossref, Google Scholar
- 21. , Regular subgraphs of hypercubes, Ars Combin. 52 (1999) 21–32. Google Scholar
- 22. , Strong Menger connectivity with conditional faults on the class of hypercube-like networks, Inform. Process. Lett. 106 (2008) 64–69. Crossref, ISI, Google Scholar
- 23. , Connectivity of Cartesian product of graphs, Appl. Math. Lett. 21 (2008) 682–685. Crossref, Google Scholar
- 24. , Embedding long paths in k-ary n-cubes with faulty nodes and links, IEEE Trans. Parallel Distrib. Syst. 19 (2008) 1071–1085. Google Scholar
- 25. , Panconnectivity of n-dimensional torus networks with faulty vertices and edges, Discrete Appl. Math. 161 (2013) 404–423. Crossref, Google Scholar


