A ROUTING ALGORITHM FOR THE CAYLEY GRAPHS GENERATED BY PERMUTATION GROUPS

A construction is given of an infinite family of finite self-complementary, vertex-transitive graphs which are not Cayley graphs. To the authors' knowledge, these are the first known examples of such graphs. The nature of the construction was suggested by a general study of the structure of self-complementary, vertex-transitive graphs. It involves the product action of a wreath product of permutation groups.

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Symmetry in interconnection networks based on Cayley graphs of permutation groups: A survey

Parallel Computing ◽

10.1016/0167-8191(93)90054-o ◽

1993 ◽

Vol 19 (4) ◽

pp. 361-407 ◽

Cited By ~ 204

Author(s):

S Lakshmivarahan ◽

Jung-Sing Jwo ◽

S.K Dhall

Keyword(s):

Interconnection Networks ◽

Cayley Graphs ◽

Permutation Groups

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REGULAR PERMUTATION GROUPS AND CAYLEY GRAPHS

European Women in Mathematics ◽

10.1142/9789814277686_0003 ◽

2009 ◽

Author(s):

CHERYL E. PRAEGER

Keyword(s):

Cayley Graphs ◽

Permutation Groups

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Distributed and Fault-Tolerant Routing for Borel Cayley Graphs

International Journal of Distributed Sensor Networks ◽

10.1155/2012/124245 ◽

2012 ◽

Vol 8 (10) ◽

pp. 124245 ◽

Cited By ~ 1

Author(s):

Junghun Ryu ◽

Eric Noel ◽

K. Wendy Tang

Keyword(s):

Interconnection Networks ◽

Fault Tolerant ◽

Cayley Graphs ◽

Routing Algorithm ◽

Topology Change ◽

Link Failures ◽

End To End Delay ◽

Low Degree ◽

Transitivity Property ◽

Path Lengths

We explore the use of a pseudorandom graph family, Borel Cayley graph family, as the network topology with thousands of nodes operating in a packet switching environment. BCGs are known to be an efficient topology in interconnection networks because of their small diameters, short average path lengths, and low-degree connections. However, the application of BCGs is hindered by a lack of size flexibility and fault-tolerant routing. We propose a fault-tolerant routing algorithm for BCGs. Our algorithm exploits the vertex-transitivity property of Borel Cayley graphs and relies on extra information to reflect topology change. Our results show that the proposed method supports good reachability and a small End-to-End delay under various link failures scenarios.

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NEW CONSTRUCTIONS OF SELF-COMPLEMENTARY CAYLEY GRAPHS

Journal of the Australian Mathematical Society ◽

10.1017/s1446788720000488 ◽

2021 ◽

pp. 1-14

Author(s):

CAI HENG LI ◽

GUANG RAO ◽

SHU JIAO SONG

Keyword(s):

Cayley Graphs ◽

Permutation Groups ◽

Product Action ◽

Generic Construction ◽

Action Type ◽

Vertex Primitive

Abstract Vertex-primitive self-complementary graphs were proved to be affine or in product action by Guralnick et al. [‘On orbital partitions and exceptionality of primitive permutation groups’, Trans. Amer. Math. Soc.356 (2004), 4857–4872]. The product action type is known in some sense. In this paper, we provide a generic construction for the affine case and several families of new self-complementary Cayley graphs are constructed.

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Cubic Cayley graphs with small diameter.

Discrete Mathematics & Theoretical Computer Science ◽

10.46298/dmtcs.285 ◽

2001 ◽

Vol Vol. 4 no. 2 ◽

Author(s):

Eugene Curtin

Keyword(s):

Symmetric Group ◽

Cayley Graphs ◽

Small Diameter ◽

Permutation Groups ◽

Large Graphs ◽

Polya's Theorem ◽

International Audience ◽

Pólya’S Theorem

International audience In this paper we apply Polya's Theorem to the problem of enumerating Cayley graphs on permutation groups up to isomorphisms induced by conjugacy in the symmetric group. We report the results of a search of all three-regular Cayley graphs on permutation groups of degree at most nine for small diameter graphs. We explore several methods of constructing covering graphs of these Cayley graphs. Examples of large graphs with small diameter are obtained.

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