A survey on recurrence relations for the independence polynomial of hypergraphs

TL;DR

This survey explores various recurrence relations for the independence polynomial of hypergraphs, extending known relations from simple graphs and introducing new ones through vertex and edge operations.

Contribution

It provides a comprehensive overview of recurrence relations for hypergraph independence polynomials, including an extension of the classic relation from simple graphs and novel relations.

Findings

Extension of recurrence relation from simple graphs to hypergraphs

Introduction of new recurrence relations for hypergraph independence polynomials

Discussion of vertex and edge operations affecting the polynomial

Abstract

The independence polynomial of a hypergraph is the generating function for its independent (vertex) sets with respect to their cardinality. This article aims to discuss several recurrence relations for the independence polynomial using some vertex and edge operations. Further, an extension of the well-known recurrence relation for simple graphs to hypergraphs is proven and other novel recurrence relations are also discussed.