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Isomorphic factorization of the complete graph into Cayley digraphs

✍ Scribed by G. L. Chia; Poh-Hwa Ong

Publisher: John Wiley and Sons
Year: 2006
Tongue: English
Weight: 151 KB
Volume: 52
Category: Article
ISSN: 0364-9024
DOI: 10.1002/jgt.20159

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✦ Synopsis

Abstract

Let Z~p~ denote the cyclic group of order p where p is a prime number. Let X = X(Z~p~, H) denote the Cayley digraph of Z~p~ with respect to the symbol H. We obtain a necessary and sufficient condition on H so that the complete graph on p vertices can be edge‐partitioned into three copies of Cayley digraphs of the same group Z~p~ each isomorphic to X. Based on this condition on H, we then enumerate all such Cayley graphs and digraphs. © 2006 Wiley Periodicals, Inc. J Graph Theory 52: 243–256, 2006

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