# Construction numbers: How to build a graph?

## TL;DR

This paper investigates the construction sequences of graphs, defining the construction number as the count of valid sequences, and computes this number for various graph families to understand their structural properties.

## Contribution

It introduces the concept of construction numbers for graphs and provides formulas for calculating them across different graph families, advancing graph enumeration methods.

## Key findings

- Determined construction numbers for several graph families.
- Established formulas for counting valid construction sequences.
- Enhanced understanding of graph structural enumeration.

## Abstract

A construction sequence for a graph is a listing of the elements of the graph (the set of vertices and edges) such that each edge follows both its endpoints. The construction number of the graph is the number of such sequences. We determine this number for various graph families.