Isomorphic and Nonisomorphic, Isospectral Circulant Graphs
نویسنده
چکیده
New criteria for which Cayley graphs of cyclic groups of any order can be completely determined–up to isomorphism–by the eigenvalues of their adjacency matrices is presented. Secondly, a new construction for pairs of nonisomorphic Cayley graphs of cyclic groups with the same list of eigenvalues of their adjacency matrices will be presented.
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...
متن کاملGeneration of isospectral graphs
We discuss a discrete version of Sunada's Theorem on isospectral manifolds which allows to generate isospectral simple graphs, i.e. nonisomorphic simple graphs which have the same Laplace spectrum. We also consider additional boundary conditions and Buser's transplantation technique applied to a discrete situation.
متن کاملNonexistence of Triples of Nonisomorphic Connected Graphs with Isomorphic Connected P3-graphs
In the paper “Broersma and Hoede, Path graphs, J. Graph Theory 13 (1989) 427-444”, the authors asked a problem whether there is a triple of mutually nonisomorphic connected graphs which have an isomorphic connected P3-graph. In this paper, we show that there is no such triple, and thus completely solve this problem.
متن کاملN ov 2 00 7 Nonexistence of triples of nonisomorphic connected graphs with isomorphic connected P 3 - graphs ∗
In the paper ”Broersma and Hoede, Path graphs, J. Graph Theory 13 (1989) 427-444”, the authors proposed a problem whether there is a triple of mutually nonisomorphic connected graphs which have an isomorphic connected P3-graph. For a long time, this problem remains unanswered. In this paper, we give it a negative answer that there is no such triple, and thus completely solve this problem.
متن کاملOn the Ad am Property for Circulant Graphs
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 part...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2009