✦ LIBER ✦

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

✍ Scribed by Anne Joseph

Publisher: Elsevier Science
Year: 1995
Tongue: English
Weight: 514 KB
Volume: 141
Category: Article
ISSN: 0012-365X
DOI: 10.1016/0012-365x(93)e0215-p

No coin nor oath required. For personal study only.

✦ Synopsis

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 is isomorphic to a Cayley digraph on both 7/F2 and Yp x 2~p if and only if X is a lexicographic product of two Cayley digraphs of order p. Equivalently, there exists a subgroup H of G of order p such that for every t ~ T\H, we have tH ~_ T.

📜 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

Problem 141. : The genus of a Cayley gra

Problem 141. : The genus of a Cayley graph is the smallest genus of any surface on which the graph can be imbedded. The genus of a group G is the smallest genus of all connected Cayley graphs on G. Is it true that for each genus g, there is a group of genus g?

📂 Article 📅 1991 🏛 Elsevier Science 🌐 English ⚖ 69 KB

acceptable if they are not as widely known as they deserve.