Determining finite connected graphs along the quadratic embedding constants of paths

Edy Tri Baskoro, Nobuaki Obata

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Pages (from-to)539-560
Number of pages22
JournalElectronic Journal of Graph Theory and Applications
Volume9
Issue number2
DOIs
Publication statusPublished - 2021

Keywords

  • claw-free graphs
  • conditionally negative definite matrix
  • distance matrix
  • quadratic embedding constant
  • star product graph

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

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