PQ-type adjacency polytopes of join graphs
Hidefumi Ohsugi, Akiyoshi Tsuchiya

TL;DR
This paper studies PQ-type adjacency polytopes derived from join graphs, providing explicit formulas for their $h^*$-polynomials and normalized volumes, which are relevant for power-flow analysis in electrical networks.
Contribution
It introduces explicit formulas for the $h^*$-polynomial and normalized volume of PQ-type adjacency polytopes for join graphs, including complete multipartite and wheel graphs.
Findings
Formulas for $h^*$-polynomial of join graphs
Explicit normalized volume formulas for specific graphs
Connections to power-flow study in electrical engineering
Abstract
PQ-type adjacency polytopes are lattice polytopes arising from finite graphs . There is a connection between and the engineering problem known as power-flow study, which models the balance of electric power on a network of power generation. In particular, the normalized volume of plays a central role. In the present paper, we focus the case where is a join graph. In fact, formulas of the -polynomial and the normalized volume of of a join graph are presented. Moreover, we give explicit formulas of the -polynomial and the normalized volume of when is a complete multipartite graph or a wheel graph.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Geometric and Algebraic Topology · Advanced Differential Equations and Dynamical Systems
