Wuhan University Journal of Natural Sciences

, Volume 20, Issue 5, pp 375–380 | Cite as

Wide diameter for two families of interconnection networks

Mathematics

Abstract

Wide diameter is an important parameter for measuring the reliability and efficiency of interconnection networks. Diameter with width k of a graph G, k-diameter, is defined as the minimum integer d for which there exist at least k internally disjoint paths of length at most d between any two distinct vertices in G. In this paper, we will discuss the wide diameter of two families of interconnection networks and present the bounds of wide diameter of G(G0,G1,…,Gr−1,L), where \(L = \bigcup\limits_{i = 1}^{r - 1} {M_{i,i + 1} }\), Mi,i+1 is an arbitrary perfect matching between V (Gi) and V (Gi+1), and G(G0,G1,F), where F = {(uivi)|1 ⩽ in}∪{(uivi+1)|1 ⩽ in}, uiV(G0), viV(G1). And they are used in practical applications, especially in the distributed and parallel computer networks.

Keywords

diameter wide diameter networks 

CLC number

O 157.6 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Bondy J A, Murty U S R. Graph Theory with Applications[M]. London: Macmillan Press, 1976.Google Scholar
  2. [2]
    Hsu D F. On container width and length in graphs, groups and networks[J]. IEICE Trans Fundam, 1994, 77(4): 668–680.Google Scholar
  3. [3]
    Hsu D F, Luczak T. Note on the k -diameter of k -regular k -connected graphs[J]. Discrete Mathematics, 1994, 133(1): 291–296.Google Scholar
  4. [4]
    Hsu D F, Lyuu Y D. A graph-theoretical study of transmission delay and fault tolerance[J]. International Journal of Mini and Microcomputers, 1994, 16(1): 35–42.Google Scholar
  5. [5]
    Flandrin E, Li H. Mengerian properties, Hamiltonicity and claw-free graphs[J]. Networks, 1994, 24(3): 177–183.CrossRefGoogle Scholar
  6. [6]
    Banič I, Žerovnik J. Wide diameter of Cartesian graph bundles [J]. Discrete Mathematics, 2010, 310(12): 1697–1701.CrossRefGoogle Scholar
  7. [7]
    Xu J M. Wide-diameter of Cartesian product graphs and digraphs[J]. Journal Combinatorial Optimization, 2004, 8(2): 171–181.CrossRefGoogle Scholar
  8. [8]
    Erveš R, Žerovnik J. Wide-diameter of product graphs[J]. Fundamenta Informaticae, 2013, 125(2): 153–160.Google Scholar
  9. [9]
    Rajasingh I, Rajan B, Rajan R S. Wide diameter of generalized fat tree[C]//International Conference on Informatics Engineering and Information Science. Heidelberg: Springer-Verlag, 2011,253: 424–430.CrossRefGoogle Scholar
  10. [10]
    Chen Y C, Tan J M. Restricted connectivity for three families of interconnection networks[J]. Applied Mathematics and Computation, 2007, 188(2): 1848–1855.CrossRefGoogle Scholar
  11. [11]
    Chen Y C, Tan J J M, Hsu L H. Super-connectivity and super- edge-connectivity for some interconnection networks[J]. Applied Mathematics and Computation, 2003, 140(2-3): 245–254.CrossRefGoogle Scholar
  12. [12]
    Park J H, Lim H S, Kim H C. Panconnectivity and pancyclicity of hypercube-like interconnection networks with faulty elements[J]. Theoretical Computer Science, 2007, 377(1-3): 170–180.CrossRefGoogle Scholar
  13. [13]
    Menger K. Zur allgemeinen Kurv entheorie[J]. Fundamenta Mathemtice, 1927, 10(1): 96–115.Google Scholar
  14. [14]
    Whithey H. Congruent graphs and the connectivity of graphs[J]. Americn Jounal of Mathematics, 1932, 54: 150–68.CrossRefGoogle Scholar

Copyright information

© Wuhan University and Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.School of Mathematics and Computer ScienceHubei UniversityWuhan, HubeiChina

Personalised recommendations