On the Ad am Property for Circulant Graphs
نویسنده
چکیده
We investigate conditions for isomorphism between circulant graphs and analyze their automorphism group, with special emphasis on loop networks. We give a survey of pertinent published results and answer partially a long-standing conjecture [5] that all degree 4 circulants which are isomorphic are Ad am isomorphic. This paper also surveys solutions to several problems introduced in [9]. In particular, we show that with a restriction on chord length, degree 4 circulant graphs have the Ad am property. We also use the same method to give a simple proof of the fact that all circulant graphs with a prime number of nodes have the Ad am property.
منابع مشابه
On the spectral Ádám property for circulant graphs
We investigate a certain condition for isomorphism between circulant graphs (known as the Ad am property) in a stronger form by referring to isospectrality rather than to isomorphism of graphs. We describe a wide class of graphs for which the Ad am conjecture holds. We apply these results to establish an asymptotic formula for the number of non-isomorphic circulant graphs and connected circulan...
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