Abstract
A finite group G is said to have the m-CI property if, for any two Cayley graphs Cay(G, S) and Cay(G, T) of valency m, Cay(G, S) congruent to Cay(G, T) implies S-sigma = T for some automorphism sigma of G. In this paper, we investigate finite groups with the m-CI property. We first construct groups with the 3-CI property but not with the 2-CI property, and then prove that a nonabelian simple group has the 3-CI property if and only if it is A(5). Finally, for infinitely many values of In, we construct Frobenius groups with the m-CI property but not with the nontrivial L-CI property for any k <m.
Original language | English |
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Pages (from-to) | 253-261 |
Journal | Bulletin of the Australian Mathematical Society |
Volume | 56 |
DOIs | |
Publication status | Published - 1997 |