Linearly many faults in Cayley graphs generated by transposition trees

Abstract We prove that when linearly many vertices are deleted in a Cayley graph generated by a transposition tree, the resulting graph has a large connected component containing almost all remaining vertices.

[1]  Shietung Peng,et al.  An Efficient Algorithm for k-Pairwise Disjoint Paths in Star Graphs , 1998, Inf. Process. Lett..

[2]  Eddie Cheng,et al.  Maximal vertex-connectivity of $\overrightarrow{S_{n,k}}$ , 2005 .

[3]  Jou-Ming Chang,et al.  Panconnectivity, fault-tolerant hamiltonicity and hamiltonian-connectivity in alternating group graphs , 2004 .

[4]  Jimmy J. M. Tan,et al.  Hyper hamiltonian laceability on edge fault star graph , 2004, Inf. Sci..

[5]  Jimmy J. M. Tan,et al.  Routing properties of supercubes , 2001, Inf. Sci..

[6]  Jimmy J. M. Tan,et al.  Fault Hamiltonicity and fault Hamiltonian connectivity of the (n, k)‐star graphs , 2003, Networks.

[7]  Eddie Cheng,et al.  On the Day-Tripathi orientation of the star graphs: Connectivity , 2000, Inf. Process. Lett..

[8]  Jimmy J. M. Tan,et al.  On mutually independent hamiltonian paths , 2006, Appl. Math. Lett..

[9]  Eunseuk Oh,et al.  Hyper-Star Graph: A New Interconnection Network Improving the Network Cost of the Hypercube , 2002, EurAsia-ICT.

[10]  S. Lakshmivarahan,et al.  A new class of interconnection networks based on the alternating group , 1993, Networks.

[11]  Sarmad Abbasi.  On the genus of the star graphs , 2000, Ars Comb..

[12]  Shahram Latifi,et al.  A Well-Behaved Enumeration of Star Graphs , 1995, IEEE Trans. Parallel Distributed Syst..

[13]  Jou-Ming Chang,et al.  Distributed algorithms for finding the unique minimum distance dominating set in directed split-stars , 2003, J. Parallel Distributed Comput..

[14]  Sheldon B. Akers,et al.  The Star Graph: An Attractive Alternative to the n-Cube , 1994, ICPP.

[15]  Eddie Cheng,et al.  Unidirectional (n, k)-Star Graphs , 2002, J. Interconnect. Networks.

[16]  Eddie Cheng,et al.  Vulnerability issues of star graphs, alternating group graphs and split-stars: strength and toughness , 2002, Discret. Appl. Math..

[17]  Eddie Cheng,et al.  Structural Properties Of Hyper-Stars , 2006, Ars Comb..

[18]  Marc J. Lipman,et al.  Increasing the connectivity of the star graphs , 2002, Networks.

[19]  Khaled Day,et al.  Arrangement Graphs: A Class of Generalized Star Graphs , 1992, Inf. Process. Lett..

[20]  Sheldon B. Akers,et al.  A Group-Theoretic Model for Symmetric Interconnection Networks , 1989, IEEE Trans. Computers.

[21]  Qing Hu,et al.  The 4-Star Graph is not a Subgraph of Any Hypercube , 1993, Inf. Process. Lett..

[22]  Toru Araki.  Hyper hamiltonian laceability of Cayley graphs generated by transpositions , 2006, Networks.

[23]  Eddie Cheng,et al.  Fault Resiliency of Cayley Graphs Generated by Transpositions , 2007, Int. J. Found. Comput. Sci..

[24]  Jimmy J. M. Tan,et al.  Super-connectivity and super-edge-connectivity for some interconnection networks , 2003, Appl. Math. Comput..

[25]  Eddie Cheng,et al.  Maximal vertex‐connectivity of $\overrightarrow{S_{n,k}}$ , 2005, Networks.

[26]  Yuh-Shyan Chen,et al.  Congestion-free, dilation-2 embedding of complete binary trees into star graphs , 1999 .

[27]  Eddie Cheng,et al.  Super Connectivity of Star Graphs, Alternating Group Graphs and Split-Stars , 2001, Ars Comb..

[28]  Wei-Kuo Chiang,et al.  The (n, k)-Star Graph: A Generalized Star Graph , 1995, Inf. Process. Lett..

[29]  M. Lipman,et al.  Orienting split-stars and alternating group graphs , 2000 .

[30]  Jimmy J. M. Tan,et al.  Fault hamiltonicity of augmented cubes , 2005, Parallel Comput..

[31]  Jimmy J. M. Tan,et al.  Restricted connectivity for three families of interconnection networks , 2007, Appl. Math. Comput..

[32]  Eddie Cheng,et al.  Maximal vertex-connectivity of Sn,k , 2005 .

[33]  Yu-Chee Tseng,et al.  Congestion-free, dilation-2 embedding of complete binary trees into star graphs , 1999, Networks.

[34]  Shietung Peng,et al.  Cluster fault-tolerant routing in star graphs , 1994, Networks.

[35]  Saïd Bettayeb,et al.  On the Genus of Star Graphs , 1994, IEEE Trans. Computers.