Nobuaki Obata

collaborators

5 papers

math.CO2025

Quadratic Embedding Constants of Corona Graphs

Ferdi, Edy Tri Baskoro, Nobuaki Obata +1

The quadratic embedding constant (QEC) of a connected graph is defined to be the maximum of the quadratic function associated with its distance matrix on a certain unit sphere of c…

math.CO2025

Partial Chebyshev Polynomials and Fan Graphs

Wojciech MÅotkowski, Nobuaki Obata

Motivated by the product formula of the Chebyshev polynomials of the second kind $U_{n} (x)$ , we newly introduce the partial Chebyshev polynomials $U_{n}^{e} (x)$ and $U^{\mathr…

math.CO2025

Quadratic Embedding Constants of Strongly Regular Graphs

Nobuaki Obata

We obtain an explicit formula for the quadratic embedding constant (QEC) of a strongly regular graph $srg (n, k, I^», I^¼)$ with $I^¼ \geq 1$ . By using QEC we give a necessary and s…

math.CO2024

Quadratic embedding constants of fan graphs and graph joins

Wojciech MÅotkowski, Nobuaki Obata

We derive a general formula for the quadratic embedding constant of a graph join $K ˉ_{m} + G$ , where $K ˉ_{m}$ is the empty graph on $m \geq 1$ vertices and $G$ is an arbitrary gra…

math.PR2024

Meixner random variables and their quantum operators

Nobuaki Obata, Aurel I. Stan, Hiroaki Yoshida

We find the position-momentum decomposition of the quantum operators of the classic Meixner random variables. The position-momentum decomposition involves translation operators, wh…