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IEICE TRANSACTIONS on Fundamentals

Cayley Graph Representation and Graph Product Representation of Hypercubes

Miya MOROTA, Ryoichi HATAYAMA, Yukio SHIBATA

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Summary :

Hypercube Qn is a well-known graph structure having three different kinds of equivalent definitions that are: 1. binary n bit sequences with the adjacency condition, 2. Q1=K2, Qn=Qn-1 K2, where means the Cartesian product, 3. the Cayley graph on Z2n with the generator set {100, 0100, , 001}. We give a necessary and sufficient condition for a set of binary sequences to be a generator set for the hypercube. Then, we give relations between some generator sets and relational products. These results show the wide variety of representability of hypercubes which would be used for many applications.

Publication
IEICE TRANSACTIONS on Fundamentals Vol.E94-A No.3 pp.946-954
Publication Date
2011/03/01
Publicized
Online ISSN
1745-1337
DOI
10.1587/transfun.E94.A.946
Type of Manuscript
PAPER
Category
Graphs and Networks

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