» » Relationships among popular interconnection Networks: Generalization of Cayley Graphs Generated by Transposition Trees Connectivity, Decomposition and Orientation

Download Relationships among popular interconnection Networks: Generalization of Cayley Graphs Generated by Transposition Trees Connectivity, Decomposition and Orientation fb2

by Nart SHAWASH
Download Relationships among popular interconnection Networks: Generalization of Cayley Graphs Generated by Transposition Trees Connectivity, Decomposition and Orientation fb2
Science & Mathematics
  • Author:
    Nart SHAWASH
  • ISBN:
    3639187385
  • ISBN13:
    978-3639187380
  • Genre:
  • Publisher:
    VDM Verlag (August 18, 2009)
  • Pages:
    172 pages
  • Subcategory:
    Science & Mathematics
  • Language:
  • FB2 format
    1928 kb
  • ePUB format
    1630 kb
  • DJVU format
    1563 kb
  • Rating:
    4.7
  • Votes:
    223
  • Formats:
    doc docx txt lit


The Cayley graph Cay(S n, S) on the symmetric group has an important role for the study of Cayley graphs as interconnection networks. In this paper, we show that the Cayley graph generated by a transposition set is vertex-bipancyclic if and only if it is not the star graph.

The Cayley graph Cay(S n, S) on the symmetric group has an important role for the study of Cayley graphs as interconnection networks. We also provide a necessary and sufficient condition for Cay(S n, S) to be edge-bipancyclic.

The class of star graphs is a special case of Cayley graphs generated by. .Structural properties of Cayley graphs generated by transposition trees.

The class of star graphs is a special case of Cayley graphs generated by transposition trees. In this paper, we give directions on these graphs and study the connectivity properties of the resulting unidirectional graphs. Conditional connectivity of star graph networks under embedding restriction. Yuxing Yang, Shiying Wang. Successive Generalizations of Star Graphs. Eddie Cheng, Nart Shawash. 2012 12th International Symposium on Pervasive Systems, Algorithms and Networks.

The star graph and the alternating group graph were introduced as competitive . Orienting Cayley graphs generated by transposition trees. Hyper hamiltonian laceability of Cayley graphs generated by transpositions.

The star graph and the alternating group graph were introduced as competitive alternatives to the hypercube, and they are indeed superior over the hypercube under many measures. However, they do suffer from scaling issues. To address this, different generalizations, namely, the (n,k)-star graph and the arrangement graph were introduced to address this shortcoming. Eddie Cheng, László Lipták, Nart Shawash. Computers & Mathematics with Applications.

The generalized connectivity of a graph is a natural generalization of the connectivity and can serve for . The study of Cayley graphs has many applications in the field of design and analysis of interconnection networks.

The generalized connectivity of a graph is a natural generalization of the connectivity and can serve for measuring the capability of a network G to connect any k vertices in G. Given a graph. Let Sym(n) be the group of all permutations on ({1,ldots,n}) and ({mathcal {T}}) be a set of transpositions of Sym(n). Let (G({mathcal {T}})) be the graph on n vertices ({1,2,ldots,n}) such that there is an edge ij in (G({mathcal {T}})). if and only if the transposition (in {mathcal {T}}).

Subjects: Combinatorics (math.

In mathematics and computer science, connectivity is one of the basic concepts of graph theory: it asks for the minimum number of elements (nodes or edges) that need to be removed to separate the remaining nodes into isolated subgraphs. It is closely related to the theory of network flow problems. The connectivity of a graph is an important measure of its resilience as a network.

cube graph that was proposed as a topology for interconnection networks.

This result is a common generalization of previous results by Feng, Ganesan, Harary, Mirafzal, and Zhang and Huang. As another special case, we obtain the automorphism group of the extended cube graph that was proposed as a topology for interconnection networks.

Книги Furthermore, a study attempting to find neural correlates of magnetic navigation will be presented. Despite the evidence in favor of magnetic navigation in pigeons, the magnetic stimulation was not represented in the activity of the cells. This monograph provides an overview of this understanding, with a focus on the use of magnetic information in the homing flight of pigeons. Homing pigeons have the remarkable skill to find their home when released at distant sites. Great advances in the understanding of how they are able to navigate so reliably have been made in the last century.

Cayley graphs have been well-studied as a model for interconnection networks due to their low diameter, optimal fault . A problem of practical and theoretical interest is to determine or estimate the diameter of Cayley graphs.

Cayley graphs have been well-studied as a model for interconnection networks due to their low diameter, optimal fault tolerance, and algorithmic efficiency, among other properties.

Star generated graphs were proposed as an attractive alternative to hypercubes for massive parallel computing in early 1980s, due to sublogarithmic regularity and diameter. However, star graphs suffer from n! vertices. As the gaps between (n-1)! and n! grow too fast to be considered for practical implementation. (n,k)-Arrangement graphs and (n,k)-Star graphs were proposed as a remedy for n! problem. Star graphs are one extreme case in a general class of Cayley graphs generated by transposition trees. This work generalizes Cayley graphs generated by transposition trees to a class that contains both (n,k)-Arrangement graphs and (n,k)-Star graphs as special cases. Moreover connectivity properties, decomposition methods, relationships among different classes of interconnection networks and local orientation rules are derived. Finally, even more general and flexible class of interconnection networks is introduced.