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Quadratic embedding constants of lexicographic product graphs.

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Τίτλος: Quadratic embedding constants of lexicographic product graphs.
Συγγραφείς: Mou, Guiqiang1 (AUTHOR) guiqiang.mou@csu.edu.cn
Πηγή: Linear Algebra & its Applications. Oct2026, Vol. 746, p1-17. 17p.
Θεματικοί όροι: *Complete graphs, *Regular graphs, *Matrices (Mathematics), *Bipartite graphs, *Graph theory, *Quadratic forms
Περίληψη: The quadratic embedding constant of a finite and connected graph G , denoted by QEC(G), is defined as the maximum of the quadratic form of the distance matrix of G on the subset of the unit sphere orthogonal to the all-ones vector. In this paper, we study the QEC of lexicographic product graphs, and establish general formulas for QEC (G [ H ]) when one factor is a complete graph or a complete bipartite graph. In particular, when the other factor is a regular graph, we derive explicit formulas for QEC (G [ H ]). [ABSTRACT FROM AUTHOR]
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  Data: Quadratic embedding constants of lexicographic product graphs.
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  Data: *<searchLink fieldCode="DE" term="%22Complete+graphs%22">Complete graphs</searchLink><br />*<searchLink fieldCode="DE" term="%22Regular+graphs%22">Regular graphs</searchLink><br />*<searchLink fieldCode="DE" term="%22Matrices+%28Mathematics%29%22">Matrices (Mathematics)</searchLink><br />*<searchLink fieldCode="DE" term="%22Bipartite+graphs%22">Bipartite graphs</searchLink><br />*<searchLink fieldCode="DE" term="%22Graph+theory%22">Graph theory</searchLink><br />*<searchLink fieldCode="DE" term="%22Quadratic+forms%22">Quadratic forms</searchLink>
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  Data: The quadratic embedding constant of a finite and connected graph G , denoted by QEC(G), is defined as the maximum of the quadratic form of the distance matrix of G on the subset of the unit sphere orthogonal to the all-ones vector. In this paper, we study the QEC of lexicographic product graphs, and establish general formulas for QEC (G [ H ]) when one factor is a complete graph or a complete bipartite graph. In particular, when the other factor is a regular graph, we derive explicit formulas for QEC (G [ H ]). [ABSTRACT FROM AUTHOR]
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        Value: 10.1016/j.laa.2026.05.012
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      – Code: eng
        Text: English
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        Type: general
      – SubjectFull: Regular graphs
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      – SubjectFull: Matrices (Mathematics)
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      – TitleFull: Quadratic embedding constants of lexicographic product graphs.
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              Text: Oct2026
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              Y: 2026
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