@article{d929a9b1869a4614b3f9ea340f4b4622,
title = "On quadratic embedding constants of star product graphs",
abstract = "A connected graph G 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 equivalently if the quadratic embedding constant QEC(G) is non-positive. For a finite star product of (finite or infinite) graphs G = G1 *...* Gr an estimate of QEC(G) is obtained after a detailed analysis of the minimal solution of a certain algebraic equation. For the path graph Pn an implicit formula for QEC(Pn) is derived, and by limit argument QEC(Z) = QEC(Z+) =-1=2 is shown. During the discussion a new integer sequence is found.",
keywords = "Conditionally negative definite matrix, Distance matrix, QE constant, Quadratic embedding, Star product graph",
author = "Wojciech Mlotkowski and Nobuaki Obata",
note = "Funding Information: WM is supported by NCN grant 2016/21/B/ST1/00628. NO is supported by JSPS Grant-in-Aid for Scientific Research No. 16H03939 and No. 19H01789. He thanks the Institute of Mathemat-ics, University of Wroc law for their kind hospitality. We acknowledge the referee's motivating suggestion for the estimates in the proof of Proposition 5.2. Funding Information: 00628. NO is supported by JSPS Gran t-in-Aid for Scien tific Researc h No.16H03939 and No.19H01789. He thanks the Institute of Mathematics, University of Wroc law for their kind hospitalit y. We acknowledge the referee{\textquoteright}s motiv ating suggestion for the estimates in the proof of Proposition 5.2. Publisher Copyright: {\textcopyright} 2020, Hokkaido University.",
year = "2020",
doi = "10.14492/hokmj/1591085015",
language = "English",
volume = "49",
pages = "129--163",
journal = "Hokkaido Mathematical Journal",
issn = "0385-4035",
publisher = "Department of Mathematics, Hokkaido University",
number = "1",
}