Super connectivity of balanced hypercubes

Abstract The reliability of an interconnection network is an important issue for multiprocessor systems. In this paper, we study a reliability measure, called super connectivity, in the balanced hypercube BH n , which is a variant of the hypercube. We show that the super connectivity of BH n is 4 n - 4 and the super edge-connectivity of BH n is 4 n - 2 for n ⩾ 2 . That is, to become a disconnected graph containing no isolated vertex, we need to remove at least 4 n - 4 vertices (resp. 4 n - 2 edges) from BH n .

[1]  David Huygens,et al.  Integer programming formulations for the two 4-hop-constrained paths problem , 2007 .

[2]  Bih-Sheue Shieh,et al.  On connectivity of the Cartesian product of two graphs , 1999, Appl. Math. Comput..

[3]  Abdol-Hossein Esfahanian,et al.  Generalized Measures of Fault Tolerance with Application to N-Cube Networks , 1989, IEEE Trans. Computers.

[4]  Meijie Ma,et al.  The super connectivity of exchanged hypercubes , 2011, Inf. Process. Lett..

[5]  F. Boesch.  Synthesis of reliable networks - a survey , 1986, IEEE Transactions on Reliability.

[6]  Ming-Chien Yang,et al.  Bipanconnectivity of balanced hypercubes , 2010, Comput. Math. Appl..

[7]  Jie Wu,et al.  The Balanced Hypercube: A Cube-Based System for Fault-Tolerant Applications , 1997, IEEE Trans. Computers.

[8]  Jie Wu,et al.  Balanced Hypercubes , 1992, ICPP.

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

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

[11]  Jun-Ming Xu,et al.  Super connectivity of line graphs , 2005, Inf. Process. Lett..

[12]  Jun-Ming Xu,et al.  Edge-pancyclicity and Hamiltonian laceability of the balanced hypercubes , 2007, Appl. Math. Comput..

[13]  Jie Wu,et al.  AREA EFFICIENT LAYOUT OF BALANCED HYPERCUBES , 1995 .

[14]  Chengfu Qin,et al.  Super connectivity of Kronecker products of graphs , 2010, Inf. Process. Lett..

[15]  Jun-Ming Xu,et al.  The super connectivity of augmented cubes , 2008, Inf. Process. Lett..

[16]  Jun-Ming Xu,et al.  On super edge‐connectivity of Cartesian product graphs , 2007, Networks.