✦ LIBER ✦

Isomorphism problem for Cayley graphs of Zp3

✍ Scribed by Edward Dobson

Publisher: Elsevier Science
Year: 1995
Tongue: English
Weight: 389 KB
Volume: 147
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(95)00099-i

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✦ Synopsis

We prove that if two Cayley graphs of Z~ are isomorphic, then they are isomorphic by a group automorphism of Z 3.

In [3], Babai and Frankl conjectured that Z 3 is a CI-group with respect to graphs for all primes p and k >t 1. The case k = 1 was settled positively by several authors [1,3,5,6]. It was shown by Godsil [7] that the conjecture is true for k = 2. Recently, Nowitz [8] gave an example showing that Z k is not a CI-group with respect to graphs for all k >~ 6, and asked if there existed a prime Po so that ifp t> Po and p is prime, then Z 3 is not a CI-group with respect to graphs. We will answer this question negatively by showing that Z 3 is a CI-group with respect to graphs for all primes p. This work was done towards partial completion of a Ph.D. degree at Louisiana State University under the supervision of Professor B61a Bollobhs.

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