@article{8e468e4ad8d44f6fb6bc9424308c1ed0,

title = "Determining finite connected graphs along the quadratic embedding constants of paths",

abstract = "The QE constant of a finite connected graph G, denoted by QEC(G), is by definition the maximum of the quadratic function associated to the distance matrix on a certain sphere of codimension two. We prove that the QE constants of paths Pn ≤ form a strictly increasing sequence converging to −1/2. Then we formulate the problem of determining all the graphs G satisfying QEC(Pn) QEC(G) < QEC(Pn+1). The answer is given for n= 2 and n= 3 by exploiting forbidden subgraphs for QEC(G) < 1/ 2 and the explicit QE constants of star products of the complete graphs.",

keywords = "claw-free graphs, conditionally negative definite matrix, distance matrix, quadratic embedding constant, star product graph",

author = "Baskoro, {Edy Tri} and Nobuaki Obata",

note = "Funding Information: The second author thanks Institut Teknologi Bandung for their kind hospitality, where this work was completed in March 2019. The support by JSPS Open Partnership Joint Research Project “Extremal graph theory, algebraic graph theory and mathematical approach to network science” (2017–18) is gratefully acknowledged. He also thanks Professor J. Koolen for a stimulating discussion. Funding Information: The second author thanks Institut Teknologi Bandung for their kind hospitality, where this work was completed in March 2019. The support by JSPS Open Partnership Joint Research Project ?Extremal graph theory, algebraic graph theory and mathematical approach to network science? (2017?18) is gratefully acknowledged. He also thanks Professor J. Koolen for a stimulating discussion. Publisher Copyright: {\textcopyright} 2021",

year = "2021",

doi = "10.5614/ejgta.2021.9.2.23",

language = "English",

volume = "9",

pages = "539--560",

journal = "Electronic Journal of Graph Theory and Applications",

issn = "2338-2287",

publisher = "Indonesian Combinatorics Society",

number = "2",

}