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All Journal Electronic Journal of Graph Theory and Applications (EJGTA)
Nobuaki Obata
Graduate School of Information Sciences Tohoku University Sendai 980-8579 Japan
Electrical & Electronics Engineering

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Determining finite connected graphs along the quadratic embedding constants of paths Edy Tri Baskoro; Nobuaki Obata
Electronic Journal of Graph Theory and Applications (EJGTA) Vol 9, No 2 (2021): Electronic Journal of Graph Theory and Applications
Publisher : GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.5614/ejgta.2021.9.2.23

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.
Co-Authors Edy Tri Baskoro