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Normalized
volumes of type-PQ adjacency polytopes for certain classes of
graphs
Robert Davis, Joakim Jakovleski and Qizhe Pan |
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Vol. 17 (2024), No. 3, 425–440
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Abstract |
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The type-PQ adjacency polytope associated to a simple graph is a -polytope containing valuable information about an underlying power network. Chen and the first author have recently demonstrated that, when the underlying graph is connected, the normalized volumes of the adjacency polytopes can be computed by counting sequences of nonnegative integers satisfying certain restrictions determined by . This article builds upon their work, namely by showing that one of their main results — the so-called “triangle recurrence” — applies in a more general setting. Formulas for the normalized volumes when is obtained by deleting a path or a cycle from a complete graph are also established. |
Keywords
lattice polytopes, draconian sequences
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Mathematical Subject Classification
Primary: 05A15
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Milestones
Received: 21 February 2022
Revised: 21 March 2023
Accepted: 20 April 2023
Published: 17 July 2024
Communicated by Kenneth S. Berenhaut
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Authors |
| Robert Davis | |
| Department of Mathematics Colgate University Hamilton, NY United States |
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| Joakim Jakovleski | |
| Department of Mathematics Colgate University Hamilton, NY United States |
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| Qizhe Pan | |
| Department of Mathematics Colgate University Hamilton, NY United States |
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| © 2024 MSP (Mathematical Sciences Publishers). |
