Determining finite connected graphs along the quadratic embedding constants of paths
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 w...
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| Format: | EJournal Article |
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GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB,
2021-10-16.
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| LEADER | 02125 am a22002653u 4500 | ||
|---|---|---|---|
| 001 | EJGTA_1401_pdf_198 | ||
| 042 | |a dc | ||
| 100 | 1 | 0 | |a Baskoro, Edy Tri; Combinatorial Mathematics Research Group Faculty of Mathematics and Natural Sciences Institut Teknologi Bandung Indonesia |e author |
| 100 | 1 | 0 | |a JSPS Open Partnership Joint Research Project |e contributor |
| 700 | 1 | 0 | |a Obata, Nobuaki; Graduate School of Information Sciences Tohoku University Send |e author |
| 245 | 0 | 0 | |a Determining finite connected graphs along the quadratic embedding constants of paths |
| 260 | |b GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB, |c 2021-10-16. | ||
| 500 | |a https://www.ejgta.org/index.php/ejgta/article/view/1401 | ||
| 520 | |a 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. | ||
| 540 | |a Copyright (c) 2021 Electronic Journal of Graph Theory and Applications (EJGTA) | ||
| 546 | |a eng | ||
| 690 | |a conditionally negative definite matrix; claw-free graphs; distance matrix; quadratic embedding constant; star product graph | ||
| 690 | |a 05C50; 05C12; 05C76 | ||
| 655 | 7 | |a info:eu-repo/semantics/article |2 local | |
| 655 | 7 | |a info:eu-repo/semantics/publishedVersion |2 local | |
| 655 | 7 | |a Peer-reviewed Article |2 local | |
| 786 | 0 | |n Electronic Journal of Graph Theory and Applications (EJGTA); Vol 9, No 2 (2021): Electronic Journal of Graph Theory and Applications; 539 - 560 | |
| 786 | 0 | |n 2338-2287 | |
| 787 | 0 | |n https://www.ejgta.org/index.php/ejgta/article/view/1401/pdf_198 | |
| 856 | 4 | 1 | |u https://www.ejgta.org/index.php/ejgta/article/view/1401/pdf_198 |z Get Fulltext |