How to Build a Graph in n Days: Some Variants on Graph Assembly

TL;DR

This paper extends the concept of assembly trees for graphs, providing a more generalized framework for understanding graph construction processes, building on prior work by Bona and Vince.

Contribution

It introduces a broader definition of assembly trees and explores their properties, advancing the theoretical understanding of graph assembly methods.

Findings

Generalized assembly tree definition established

Extended analysis of assembly tree properties

Connections to graph construction processes

Abstract

In a recent article by M. Bona and A. Vince, the authors introduced the concept of an assembly tree for a graph. Assembly trees act as record keeping devices for the construction of a given graph from its vertices. In this paper we extend the work initiated by M. Bona and A. Vince as well as define and examine a more generalized definition of assembly tree.