A class of fixed-degree Cayley-graph interconnection networks derived by pruning k-ary n-cubes

2002 ◽  
Author(s):  
Ding-Ming Kwai ◽  
B. Parhami
Keyword(s):  
Cayley Graph ◽  
Interconnection Networks ◽  
Fixed Degree

scholarly journals Some exact values for the diameter in Cayley graph Hl,p

2019 ◽  
Author(s):  
Caroline Patrão ◽  
Luis Kowada ◽  
Diane Castonguay ◽  
André Ribeiro ◽  
Celina Figueiredo
Keyword(s):  
Cayley Graph ◽  
Lower Bounds ◽  
Interconnection Networks ◽  
The Family ◽  
The Difference

The family of graphs H,p has been defined in the context of edge partitions. The established properties such as vertex transitivity and low diameter suggest this family as a good topology for the design of interconnection networks. The vertices of the graphH p are the tuples with values between 0 and p1, such that the sum of the values is a multiple of p, and there is an edge between two vertices, if the two corresponding tuples have two pairs of entries whose values differ by one unit. In order to work towards the diameter, the difference between an upper and a lower bounds is established to be at most and we present subfamilies of graphs H p such that, for several values of and p, the bounds are tight.

scholarly journals FROBENIUS CIRCULANT GRAPHS OF VALENCY FOUR

2008 ◽  
Vol 85 (2) ◽  
pp. 269-282 ◽  
Author(s):  
ALISON THOMSON ◽  
SANMING ZHOU
Keyword(s):  
Cayley Graph ◽  
Cyclic Group ◽  
Interconnection Networks ◽  
Frobenius Group ◽  
Optimal Routing ◽  
Circulant Graph ◽  
Circulant Graphs ◽  
Frobenius Kernel ◽  
Even Order

AbstractA first kind Frobenius graph is a Cayley graph Cay(K,S) on the Frobenius kernel of a Frobenius group $K \rtimes H$ such that S=aH for some a∈K with 〈aH〉=K, where H is of even order or a is an involution. It is known that such graphs admit ‘perfect’ routing and gossiping schemes. A circulant graph is a Cayley graph on a cyclic group of order at least three. Since circulant graphs are widely used as models for interconnection networks, it is thus highly desirable to characterize those which are Frobenius of the first kind. In this paper we first give such a characterization for connected 4-valent circulant graphs, and then describe optimal routing and gossiping schemes for those which are first kind Frobenius graphs. Examples of such graphs include the 4-valent circulant graph with a given diameter and maximum possible order.

scholarly journals Hamiltonian properties on a class of circulant interconnection networks

Filomat ◽  
2018 ◽  
Vol 32 (1) ◽  
pp. 71-85 ◽  
Author(s):  
Milan Basic
Keyword(s):  
Cayley Graph ◽  
Interconnection Networks ◽  
Interconnection Network ◽  
Cayley Graphs ◽  
Small Diameter ◽  
Quantum Spin ◽  
Perfect State ◽  
Circulant Graphs ◽  
Hamiltonian Paths ◽  
Unitary Cayley Graph

Classes of circulant graphs play an important role in modeling interconnection networks in parallel and distributed computing. They also find applications in modeling quantum spin networks supporting the perfect state transfer. It has been noticed that unitary Cayley graphs as a class of circulant graphs possess many good properties such as small diameter, mirror symmetry, recursive structure, regularity, etc. and therefore can serve as a model for efficient interconnection networks. In this paper we go a step further and analyze some other characteristics of unitary Cayley graphs important for the modeling of a good interconnection network. We show that all unitary Cayley graphs are hamiltonian. More precisely, every unitary Cayley graph is hamiltonian-laceable (up to one exception for X6) if it is bipartite, and hamiltonianconnected if it is not. We prove this by presenting an explicit construction of hamiltonian paths on Xnm using the hamiltonian paths on Xn and Xm for gcd(n,m) = 1. Moreover, we also prove that every unitary Cayley graph is bipancyclic and every nonbipartite unitary Cayley graph is pancyclic.

UPPER BOUNDS FOR SORTING PERMUTATIONS WITH A TRANSPOSITION TREE

2013 ◽  
Vol 05 (01) ◽  
pp. 1350003 ◽  
Author(s):  
BHADRACHALAM CHITTURI
Keyword(s):  
Cayley Graph ◽  
Upper Bound ◽  
Interconnection Networks ◽  
Upper Bounds

An upper bound for sorting permutations with an operation estimates the diameter of the corresponding Cayley graph and an exact upper bound equals the diameter. Computing tight upper bounds for various operations is of theoretical and practical (e.g., interconnection networks, genetics) interest. Akers and Krishnamurthy gave a Ω(n! n2) time method that examines n! permutations to compute an upper bound, f(Γ), to sort any permutation with a given transposition tree T, where Γ is the Cayley graph corresponding to T. We compute two intuitive upper bounds γ and δ′ each in O(n2) time for the same, by working solely with the transposition tree. Recently, Ganesan computed β, an estimate of the exact upper bound for the same, in O(n2) time. Our upper bounds are tighter than f(Γ) and β, on average and in most of the cases. For a class of trees, we prove that the new upper bounds are tighter than β and f(Γ).

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