Basic enumeration of graph compositions with a restricted number of components

TL;DR

This paper explores graph compositions with a limited number of components, establishing a connection to Stirling numbers of the second kind, and contributes to understanding their combinatorial properties.

Contribution

It introduces a framework for enumerating graph compositions with restricted components and links them to Stirling numbers, expanding combinatorial graph theory.

Findings

Derived formulas for counting restricted graph compositions

Connected graph compositions to Stirling numbers of the second kind

Provided combinatorial interpretations for these concepts

Abstract

The concept of graph compositions is related to several number theoretic concepts, including partitions of positive integers and the cardinality of the power set of finite sets. This paper examines graph compositions where the total number of components is restricted and illustrates a connection between graph compositions and Stirling numbers of the second kind.