✦ LIBER ✦

On the Cayley isomorphism problem

✍ Scribed by Edward Dobson

Book ID: 108315657
Publisher: Elsevier Science
Year: 2002
Tongue: English
Weight: 127 KB
Volume: 247
Category: Article
ISSN: 0012-365X
DOI: 10.1016/s0012-365x(01)00164-9

No coin nor oath required. For personal study only.

📜 SIMILAR VOLUMES

On the Isomorphism Problem for Finite Ca

On the Isomorphism Problem for Finite Cayley Graphs of Bounded Valency

✍ C.H. Li; C.E. Praeger 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 187 KB

For a subset S of a group G such that 1 / ∈ S and S = S -1 , the associated Cayley graph Cay(G, S) is the graph with vertex set G such that {x, y} is an edge if and only if yx -1 ∈ S. Each σ ∈ Aut(G) induces an isomorphism from Cay(G, S) to the Cayley graph Cay(G, S σ ). For a positive integer m, th

The isomorphism problem for Cayley digra

The isomorphism problem for Cayley digraphs on groups of prime-squared order

✍ Anne Joseph 📂 Article 📅 1995 🏛 Elsevier Science 🌐 English ⚖ 514 KB

Given any prime p, there are two non-isomorphic groups of order p2. We determine precisely when a Cayley digraph on one of these groups is isomorphic to a Cayley digraph on the other group, Namely, let X = Cay(G: T) be a Cayley digraph on a group G of order p2 with generating set T. We prove that X

Isomorphism problem for Cayley graphs of

Isomorphism problem for Cayley graphs of Zp3

✍ Edward Dobson 📂 Article 📅 1995 🏛 Elsevier Science 🌐 English ⚖ 389 KB

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 wa

On finite groups with the cayley isomorp

On finite groups with the cayley isomorphism property

✍ Li, Cai Heng; Praeger, Cheryl E.; Xu, Ming Yao 📂 Article 📅 1998 🏛 John Wiley and Sons 🌐 English ⚖ 197 KB

Let G be a finite group, and let Cay(G, S) be a Cayley digraph of G. If, for all T ⊂ G, Cay(G, S) ∼ = Cay(G, T ) implies S α = T for some α ∈ Aut(G), then Cay(G, S) is called a CI-graph of G. For a group G, if all Cayley digraphs of valency m are CI-graphs, then G is said to have the m-DCI property;

On isomorphisms of connected Cayley grap

On isomorphisms of connected Cayley graphs

✍ Li Cai Heng 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 696 KB

Let G be a finite group and Cay(G,S) the Cayley graph of G with respect to S. A subset S is called a CI-subset if, for any TCG, Cay(G,S) ~ Cay(G,T) implies S ~ = T for some ct E Aut(G). In this paper, we investigate the finite groups G in which every subset S with size at most m and (S) = G is a CI-

Isomorphic Cayley graphs on nonisomorphi

Isomorphic Cayley graphs on nonisomorphic groups

✍ Morris, Joy 📂 Article 📅 1999 🏛 John Wiley and Sons 🌐 English ⚖ 349 KB

The issue of when two Cayley digraphs on different abelian groups of prime power order can be isomorphic is examined. This had previously been determined by Anne Joseph for squares of primes; her results are extended.