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On Ádám’s conjecture for circulant graphs. (English) Zbl 0877.05040
The content of this article is analogous to the one of the author’s former paper [J. Comb. Theory, Ser. A 72, No. 1, 118-134 (1995; Zbl 0833.05063)]. Now the author proves the reviewer’s conjecture in case of an \(n\) (number of vertices) such that \(n/4\) is a square-free odd integer. A number of auxiliary results, stated in the earlier paper, is referred to. These and some new algebraic discussions (in the same style) yield together the proof of the main theorem.
The considerations in the present work constitute the completion of a trend of investigations. Our knowledge on the conjecture in question can now be summarized as follows: the conjecture is valid within the class of circulant graphs having \(n\) vertices if and only if either \(n\) or \(n/2\) or \(n/4\) is a square-free odd integer.
Unfortunately, the article appeared with a lot of inaccuracies: it contains throughout question marks instead of reference numbers.

MSC:
05C60 Isomorphism problems in graph theory (reconstruction conjecture, etc.) and homomorphisms (subgraph embedding, etc.)
05C25 Graphs and abstract algebra (groups, rings, fields, etc.)
20B25 Finite automorphism groups of algebraic, geometric, or combinatorial structures
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