|  Efe K. The crossed cube architecture for parallel computation. IEEE Transactions on Parallel and Distributed Systems, 1992, 3(5): 513-524. Chang C P, Sung T Y, Hsu L H. Edge congestion and topological properties of crossed cubes. IEEE Transactions on Parallel and Distributed Systems, 2000, 11(1): 64-80. Loh P K K, Hsu W J, Pan Y. The exchanged hypercube. IEEE Transactions on Parallel and Distributed Systems, 2005, 16(9): 866-874. Li K Q, Mu Y P, Li K Q, Min G Y. Exchanged crossed cube: A novel interconnection network for parallel computation. IEEE Transactions on Parallel and Distributed Systems, 2013, 24(11): 2211-2219. Ning W T. The super connectivity of exchanged crossed cube. Information Processing Letters, 2016, 116(2): 80-84. Ning W T, Feng X L, Wang L. The connectivity of exchanged crossed cube. Information Processing Letters, 2015, 115(2): 394-396. Auletta L, Rescigno A A, Scarano V. Embedding graphs onto the supercube. IEEE Transactions on Computers, 1995, 44(4): 593-597. Hsu H C, Li T K, Tan J J, Hsu L H. Fault hamiltonicity and fault hamiltonian connectivity of the arrangement graphs. IEEE Transactions on Computers, 2004, 53(1): 39-53. Kulasinghe P, Bettayeb S. Embedding binary trees into crossed cubes. IEEE Transactions on Computers, 1995, 44(7): 923-929. Patel A, Kusalik A, McCrosky C. Area-efficient VLSI layouts for binary hypercubes. IEEE Transactions on Computers, 2000, 49(2): 160-169. Chaudhary V, Aggarwal J K. A generalized scheme for mapping parallel algorithms. IEEE Transactions on Parallel and Distributed Systems, 1993, 4(3): 328-346. Cheng D, Hao R X, Feng Y Q. Embedding even cycles on folded hypercubes with conditional faulty edges. Information Processing Letters, 2015, 115(12): 945-949. Fan J X, Jia X H. Embedding meshes into crossed cubes. Information Sciences, 2007, 177(15): 3151-3160. Fan J X, Jia X H, Lin X L. Complete path embeddings in crossed cubes. Information Sciences, 2006, 176(22): 3332- 3346. Fan J X, Lin X L, Jia X H. Optimal path embedding in crossed cubes. IEEE Transactions on Parallel and Distributed Systems, 2005, 16(12): 1190-1200. Fu J S. Longest fault-free paths in hypercubes with vertex faults. Information Sciences, 2006, 176(7): 759-771. Kao S S, Lin C K, Huang H M, Hsu L H. Pancyclicity, panconnectivity, and panpositionability for general graphs and bipartite graphs. Ars Combinatoria, 2012, 105(105): 231-246. Tsai P Y, Lin Y T. Cycle embedding in alternating group graphs with faulty elements. In Proc. the 8th HumanCom and EMC, Aug. 2013, p.1281. Tsai C H, Lai C J. A linear algorithm for embedding of cycles in crossed cubes with edge-pancyclic. Journal of Information Science and Engineering, 2015, 31(4): 1347-1355. Wang D J. Hamiltonian embedding in crossed cubes with failed links. IEEE Transactions on Parallel and Distributed Systems, 2012, 23(11): 2117-2124. Andrews M, Chuzhoy J, Guruswami V, Khanna, S, Talwar, K, Zhang L S. Inapproximability of edge-disjoint paths and low congestion routing on undirected graphs. Combinatorica, 2010, 30(5): 485-520. Wu R Y, Chen G H, Kuo Y L, Chang G J. Node-disjoint paths in hierarchical hypercube networks. Information Sciences, 2007, 177(19): 4200-4207. Lai P L, Hsu H C. Constructing the nearly shortest path in crossed cubes. Information Sciences, 2009, 179(14): 2487- 2493. Boppana R V, Chalasani S, Raghavendra C S. Resource deadlocks and performance of wormhole multicast routing algorithms. IEEE Transactions on Parallel and Distributed Systems, 1998, 9(6): 535-549. Huang W T, Chuang Y C, Tan J J M et al. On the faulttolerant hamiltonicity of faulty crossed cubes. IEICE Transactions on Fundamentals of Electronics Communications and Computer Sciences, 2002, E85-A(6): 1359-1370. Chang T W, Navrátil O, Peng S L. The end-to-end longest path problem on a mesh with a missing vertex. Frontiers in Artificial Intelligence and Applications, 2015, 274: 59-66. Fan J X, Lin X L, Pan Y, Jia X H. Optimal fault-tolerant embedding of paths in twisted cubes. Journal of Parallel and Distributed Computing, 2007, 67(2): 205-214. Hsieh S Y. Embedding longest fault-free paths onto star graphs with more vertex faults. Theoretical Computer Science, 2005, 337(1/2/3): 370-378. Hsieh S Y, Chang N W. Hamiltonian path embedding and pancyclicity on the Möbius cube with faulty nodes and faulty edges. IEEE Transactions on Computers, 2006, 55(7): 854-863. Hsieh S Y, Lin T J. Panconnectivity and edge-pancyclicity of k-ary n-cubes. Networks, 2009, 54(1): 1-11. Lin M, Liu H M. Paths and cycles embedding on faulty enhanced hypercube networks. Acta Mathematica Scientia, 2013, 33(1): 227-246. Ma M J, Liu G Z, Xu J M. Fault-tolerant embedding of paths in crossed cubes. Theoretical Computer Science, 2008, 407(1/2/3): 110-116. Tsai C H, Jiang S Y. Path bipancyclicity of hypercubes. Information Processing Letters, 2007, 101(3): 93-97. Xu J M, Ma M J. Survey on path and cycle embedding in some networks. Frontiers of Mathematics in China, 2009, 4(2): 217-252. Bondy J A, Murty U S R. Graph Theory with Applications. Citeseer Publisher, 1976. Zhou D F, Fan J X, Lin C K, Zhou J Y, Wang X. Cycles embedding in exchanged crossed cube. International Journal of Foundations of Computer Science, 2017, 28(1): 61-76.