186 citations · 467 across the 31 of their papers we have counts for
31 papers
On the spherical design properties of a - and -polynomial association scheme
Jesse Lansdown, William J. Martin, Akihiro Munemasa +2
We show that the strength as a spherical design of the spherical embedding of a - and -polynomial association scheme with at least three classes with respect to a -polynom…
Characterizing graphs with fully positive semidefinite -matrices
Hajime Tanaka
For , the -matrix of a connected simple graph is , where denotes the path-length distance. Descr…
Multimarked Spatial Search by Continuous-Time Quantum Walk
Pedro H. G. Lugão, Renato Portugal, Mohamed Sabri +1
The quantum-walk-based spatial search problem aims to find a marked vertex using a quantum walk on a graph with marked vertices. We describe a framework for determining the computa…
The real equiangular tight frames obtained from rank graphs
Eiichi Bannai, Etsuko Bannai, Chin-Yen Lee +2
We present all nontrivial real equiangular tight frames in obtained as spherical embeddings of primitive rank graphs on vertices, and those…
Spatial Search on Johnson Graphs by Discrete-Time Quantum Walk
Hajime Tanaka, Mohamed Sabri, Renato Portugal
The spatial search problem aims to find a marked vertex of a finite graph using a dynamic with two constraints: (1) The walker has no compass and (2) the walker can check whether a…
A duality of scaffolds for translation association schemes
Xiaoye Liang, Ying-Ying Tan, Hajime Tanaka +1
Scaffolds are certain tensors arising in the study of association schemes, and have been (implicitly) understood diagrammatically as digraphs with distinguished "root" nodes and wi…