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.

primary:05C50 secondary:05C12 05C76

Original languageEnglish
JournalUnknown Journal
Publication statusPublished - 2019 Apr 16

Keywords

  • Claw-free graphs
  • Conditionally negative definite matrix
  • Distance matrix
  • Quadratic embedding constant
  • Star product graph

ASJC Scopus subject areas

  • General

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