Independent sets in certain classes of (almost) regular graphs

TL;DR

This paper enumerates independent sets in various regular and almost regular graphs, computes their generating functions, explores their connections to other combinatorial objects, and constructs bijections where possible.

Contribution

It introduces new enumeration methods for independent sets in specific graph classes and establishes relations to other combinatorial structures.

Findings

Enumerated independent sets for several graph classes

Computed generating functions for these graphs

Established bijections with other combinatorial objects

Abstract

We enumerate the independent sets of several classes of regular and almost regular graphs and compute the corresponding generating functions. We also note the relations between these graphs and other combinatorial objects and, in some cases, construct the corresponding bijections.