Normalized Volumes of Type-PQ Adjacency Polytopes for Certain Classes of Graphs

Abstract

The type-PQ adjacency polytope associated to a simple graph is a 0/1-polytope containing valuable information about an underlying power network. Chen and the first author have recently demonstrated that, when the underlying graph G is connected, the normalized volumes of the adjacency polytopes can be computed by counting sequences of nonnegative integers satisfying restrictions determined by G. 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 G is obtained by deleting a path or a cycle from a complete graph are also established.