Mathematics Quantum graphs and their spectra DARTMOUTH COLLEGE Carolyn S. Gordon RueckriemenRalfWe show that families of leafless quantum graphs that are isospectral for the standard Laplacian are finite. We show that the minimum edge length is a spectral invariant. We give an upper bound for the...
Through a number of carefully chosen examples, we demonstrate that the isomorphic nature of graphs enables both the basic properties of data observed on graphs and their descriptors (features) to be preserved throughout the data analytics process, even in the case of reordering of graph vertices,...
“The theory of graph spectra has been getting increasing attention over the last several years. … This text … moves the study further along and provides an outstanding reference for graduate students and researchers interested in the many applications of these eigenvalues and their associated eigenv...
All graphs considered in this paper are finite, simple and connected. The adjacency matrix of graphGis\(\textbf{A}(G)\)and the dimension of the nullspace of\(\textbf{A}(G)\)is thenullity,\(\eta (G)\). Anautomorphism\(\alpha \)of a graphGis a permutation\(\alpha :V(G) \right...
Spectra of Graphs: Theory and Applications, 3rd Revised and Enlarged Edition Graph \\& Groups is a research tool for computing with graphs and their automorphism groups. This note describes the various kinds of information that it can provide. DM Cvetkovic,M Doob,H Sachs,... 被引量: 27发表...
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There are several well known families of strongly regular graphs having τ=−2, and thus having one exactly positive distance eigenvalue. Examples of such graphs and their distance spectra include: 1. The cocktail party graphs CP(m) are complete multipartite graphs K2,2,…,2 on m partite ...
We recall the following theorem related to the spectral radius of graphs and their subgraphs. By ρ(G) we mean the spectral radius of G. Theorem 7 [2] Let G be a connected graph. If H is a subgraph of G, then ρ(G)≥ρ(H). Moreover the equality holds if and only if G=H. ...
Moreover, it is known thathas to be odd. All known examples for-SWRGs withsatisfyand, where Eq. (1) is automatically satisfied for all odd. Mimicking the mentioned link between SRGs and projective two-weight codes, a construction of SRWGs as coset graphs of the duals of projective three...
There are many problems in physics and chemistry where the Laplacian matrices of graphs and their spectra play the central role. Some of the applications are mentioned in Section 5. It is worth noting that the physical background served as the idea of a well known algorithm of W.T. Tutte ...