Toida's Conjecture is True

Let S be a subset of the units in Zn. Let be a circulant graph of order n (a Cayley graph of Zn) such that if ij E(), then i - j (mod n) S. Toida conjectured that if is another circulant graph of order n, then and are isomorphic if and only if they are isomorphic by a group automorphism of Zn. In this paper, we prove that Toida's conjecture is true. We further prove Zibin's conjecture, a generalisation of Toida's conjecture. In 1967,

• Type: Journal
• Year: 2002
• Where: COMBINATORICS
• Authors: Edward Dobson, Joy Morris
• Keywords: Cayley Graphs, COMBINATORICS 2002, Conjecture, Isomorphic