Generation of isospectral graphs
نویسندگان
چکیده
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.
منابع مشابه
Isospectral Graphs and Isospectral Surfaces
In memory of Hubert Pesce In this paper, we investigate the following question: to what extent is there a converse to the Theorem of Sunada Su] in the context of graphs? Our experience in dealing with the question, \Can one hear the shape of a drum?" is that the many facets of this question turn out to be surprisingly delicate. The present instance is no exception. We will rst present a partial...
متن کاملCharacterization of Isospectral Graphs Using Graph Invariants and Derived Orthogonal Parameters
Numerical graph theoretic invariants or topological indices (TIs) and principal components (PCs) derived from TIs have been used in discriminating a set of isospectral graphs. Results show that lower order connectivity and information theoretic TIs suffer from a high degree of redundancy, whereas higher order indices can characterize the graphs reasonably well. On the other hand, PCs derived fr...
متن کاملIsospectral Cayley Graphs of Some Finite Simple Groups
We apply spectral analysis of quotients of the BruhatTits buildings of type Ãd−1 to construct isospectral non-isomorphic Cayley graphs of the finite simple groups PSLd(Fq) for every d ≥ 5 (d 6= 6) and prime power q > 2.
متن کاملComputer Generation of Distance Polynomials of Graphs
A computer program is developed to compute distance polynomials of graphs containing up to 200 vertices. The code also computes the eigenvalues and the eigenvectors of the distance matrix. It requires as input only the neighborhood information from which the program constructs the distance matrix. The eigenvalues and eigenvectors are computed using the Givens-Householder method while the charac...
متن کاملThe isospectral fruits of representation theory: quantum graphs and drums
We present a method which enables one to construct isospectral objects, such as quantum graphs and drums. One aspect of the method is based on representation theory arguments which are shown and proved. The complementary part concerns techniques of assembly which are both stated generally and demonstrated. For that purpose, quantum graphs are grist to the mill. We develop the intuition that sta...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Journal of Graph Theory
دوره 31 شماره
صفحات -
تاریخ انتشار 1999