19 citations · 51 across the 13 of their papers we have counts for
13 papers
Primary Non-QE Graphs on Six Vertices
Nobuaki Obata
A connected graph is called of non-QE class if it does not admit a quadratic embedding in a Euclidean space. A non-QE graph is called primary if it does not contain a non-QE graph…
Complete Multipartite Graphs of Non-QE Class
Nobuaki Obata
We derive a formula for the QE constant of a complete multipartite graph and determine the complete multipartite graphs of non-QE class, namely, those which do not admit quadratic…
Scaling Limits for the Gibbs States on Distance-Regular Graphs with Classical Parameters
Masoumeh Koohestani, Nobuaki Obata, Hajime Tanaka
We determine the possible scaling limits in the quantum central limit theorem with respect to the Gibbs state, for a growing distance-regular graph that has so-called classical par…
Quadratic Embedding Constants of Graph Joins
Zhenzhen Lou, Nobuaki Obata, Qiongxiang Huang
The quadratic embedding constant (QE constant) of a graph is a new characteristic value of a graph defined through the distance matrix. We derive formulae for the QE constants of t…
Determining Finite Connected Graphs Along the Quadratic Embedding Constants of Paths
Edy Tri Baskoro, Nobuaki Obata
The QE constant of a finite connected graph , denoted by , is by definition the maximum of the quadratic function associated to the distance matrix on a certain…
Multivariate orthogonal polynomials: quantum decomposition, deficiency rank and support of measure
Ameur Dhahri, Nobuaki Obata, Hyun Jae Yoo
In this paper we investigate the multivariate orthogonal polynomials based on the theory of interacting Fock spaces. Our framework is on the same stream line of the recent paper by…
Asymptotic joint spectra of Cartesian powers of strongly regular graphs and bivariate Charlier-Hermite polynomials
John Vincent S. Morales, Nobuaki Obata, Hajime Tanaka
Generalizing previous work of Hora (1998) on the asymptotic spectral analysis for the Hamming graph which is the Cartesian power of the…
On Quadratic Embedding Constants of Star Product Graphs
Wojciech Młotkowski, Nobuaki Obata
A connected graph is of QE class if it admits a quadratic embedding in a Hilbert space, or equivalently if the distance matrix is conditionally negative definite, or equivalent…
Kronecker Product Graphs and Counting Walks in Restricted Lattices
Hun Hee Lee, Nobuaki Obata
Formulas are derived for counting walks in the Kronecker product of graphs, and the associated spectral distributions are obtained by the Mellin convolution of probability distribu…
Asymptotic Spectral Distributions of Distance -Graphs of Cartesian Product Graphs
Yuji Hibino, Hun Hee Lee, Nobuaki Obata
Let be a finite connected graph on two or more vertices and the distance -graph of the -fold Cartesian power of . For a fixed , we obtain explicitly…
Distance k-graphs of hypercube and q-Hermite polynomials
Hun Hee Lee, Nobuaki Obata
We will prove that some weighted graphs on the distance -graph of hypercubes approximate the -Hermite polynomial of a -gaussian variable by providing an appropriate matrix…
Localization of the Grover walks on spidernets and free Meixner laws
Norio Konno, Nobuaki Obata, Etsuo Segawa
A spidernet is a graph obtained by adding large cycles to an almost regular tree and considered as an example having intermediate properties of lattices and trees in the study of d…
Spectral Properties of the Threshold Network Model
Yusuke Ide, Norio Konno, Nobuaki Obata
We study the spectral distribution of the threshold network model.The results contain an explicit description and its asymptotic behaviour.