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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| Main Authors: | , |
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| Format: | EJournal Article |
| Published: |
GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB,
2021-10-16.
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| Online Access: | Get Fulltext |
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| Summary: | 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. |
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| Item Description: | https://www.ejgta.org/index.php/ejgta/article/view/1401 |