Abstract
In this paper we investigate some reliability measures, including super-connectivity, cyclic edge connectivity, etc., in the folded hypercubes.
Similar content being viewed by others
References
El-Amawy, A., Latifi, S.: Properties and performance of folded hypercubes. IEE. Trans. Parallel Distrib. Syst. 2(1), 31–42 (1991)
Boesch, F.T., Tindell, R.: Circulant and their connectivities. J. Graph Theory 8, 487–499 (1984)
Bondy, J.A., Murty, U.S.R.: Graph Theory with Applications. Elsevier North Holland, Amsterdam (1976)
Chang, N.W., Tsai, C.Y., Hsieh, S.Y.: On 3-extra connectivity and 3-extra edge connectivity of folded hypercubes. IEEE Trans. Comput. 63(6), 1593–1599 (2014)
Chen, Y.C., Tan, J.J.M., Hsu, L.H.: Super-connectivity and super-edge-connectivity for some interconnection networks. Appl. Math. Comput. 140, 245–254 (2003)
Esfahanian, A., Hakimi, S.: On computing a conditional edge-connectivity of a graph. Inform. Process. Lett. 27(4), 195–199 (1988)
Fu, J.S.: Fault-free cycles in folded hypercubes with more faulty elements. Inform. Process. Lett. 108(5), 261–263 (2008)
Hsieh, S.Y.: Some edge-fault-tolerant properties of the folded hypercube. Networks 52(2), 92–101 (2008)
Hsieh, S.Y., Tsai, C.Y., Chen, C.A.: Strong diagnosability and conditional diagnosability of multiprocessor systems and folded hypercubes. IEEE Trans. Computers 62(7), 1472–1477 (2012)
Imrich, W., Klavžar, S., Hammack, R.: Handbook of Product Graphs. CRC Press, Boca Raton (2011)
Li, Q.L., Li, Q.: Super edge connectivity properties of connected edge symmetric graphs. Networks 33, 147–159 (1999)
Lü, M., Chen, G.L., Xu, J.-M.: On super edge-connectivity of cartesian product graphs. Networks 49, 135–157 (2007)
Ma, M.J., Xu, J.M.: Algebraic properties and panconnectivity of folded hypercubes. Ars Combin. 95(1), 179–186 (2010)
Meng, J.: Connectivity of vertex and edge transitive graphs. Discrete Appl. Math. 127, 601–613 (2003)
Morteza Mirafzal, S.: Some other algebraic properies of folded hypercubes, arXiv:1103.4351v1 [math.GR]
Ou, J.P.: \(m\)-Restricted edge connectivity of graphs and network reliability. Xiamen University, Department of Mathematics, Ph.D. Thesis (2003)
Ou, J.P.: Edge cuts leaving components of order at least \(m\). Discrete Math. 305, 365–371 (2005)
Plummer, M.D.: On the cyclic connectivity of planar graphs. Lecture Notes in Math. 303, 235–242 (1972)
Tian, Y., Meng, J.: On super restricted edge-connetctivity of edge-transitive graphs. Discrete Math. 310, 2273–2279 (2010)
Tindell, R.: Connectivity of cayley graphs. In: Du, D.Z., Hsu, D.F. (eds.) Combinatorial Network Theory, pp. 41–64. Kluwer Academic Publishers, Amsterdam (1996)
Wang, B., Zhang, Z.: On the cyclic edge-connectivity of transitive graphs. Discret Math. 309, 4555–4563 (2009)
Xu, J.M., Ma, M.J.: Cycles in folded hypercubes. Appl. Math. Lett. 19(2), 140–145 (2006)
Xu, J.-M., Zhu, Q., Hou, X.-M., Zhou, T.: On restricted connectivity and extra connectivity of hypercubes and folded hypercubes. J. Shanghai Jiaotong Univ. Sci. 10(2), 203–207 (2005)
Yang, M.C.: Super connectivity of balanced hypercubes. Appl. Math. Comput. 219, 970–975 (2012)
Yang, W.H., Li, H.: On reliability of the folded hypercubes in terms of the extra edge-connectivity. Inf. Sci. 272, 238–243 (2014)
Yang, C., Xu, J.: Connectivity of lexicographic product and direct product of graphs. Ars Combin. 111, 3–12 (2013)
Zhang, Z., Meng, J.: On optimally-\(\lambda ^{(3)}\) transitive graphs. Discrete Appl. Math. 154, 1011–1018 (2006)
Zhang, Z., Wang, B.: Super cyclically edge-connected transitive graphs. J. Comb. Optim. 22, 549–562 (2011)
Zhang, M.M., Zhou, J.-X.: On \(g\)-extra connectivity of folded hypercubes. Theoret. Comput. Sci. 593, 146–153 (2015)
Zhou, J.-X.: Super-restricted edge-connectivity of regular edge-transitive graphs. Discrete Appl. Math. 160, 1248–1252 (2012)
Zhou, J.X.: Atoms of cyclic edge connectivity in regular graphs. J. Comb. Optim. 31, 382–395 (2014)
Zhou, J.X., Feng, Y.Q.: Super-cyclically edge-connected regular graphs. J. Comb. Optim. 26, 393–411 (2013)
Zhou, J.X., Wu, Z.L., Yang, S.C., Yuan, K.W.: Symmetric property and reliability of balanced hypercubes. IEEE Trans. Comput. 64(3), 876–881 (2015)
Zhu, Q., Xu, J.M., Hou, X.M., Xu, M.: On the reliability of the folded hypercubes. Inf. Sci. 177(8), 1782–1788 (2007)
Author information
Authors and Affiliations
Corresponding author
Additional information
Communicated by Rosihan M. Ali.
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Ghasemi, M. Some Results About the Reliability of Folded Hypercubes. Bull. Malays. Math. Sci. Soc. 44, 1093–1099 (2021). https://doi.org/10.1007/s40840-020-00999-4
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s40840-020-00999-4