Complexity of graph evolutions

TL;DR

This paper investigates the complexity of graph construction sequences by analyzing the delay and opportunity cost in permutation-based sequences, providing maximum and minimum cost sequences for various graphs to measure their building complexity.

Contribution

It introduces a method to quantify graph construction complexity through opportunity cost and provides explicit sequences for different graph types.

Findings

Maximum and minimum opportunity costs are characterized for various graphs.

The delay in edge placement serves as a measure of construction complexity.

The approach helps evaluate the efficiency of graph-building algorithms.

Abstract

A permutation of the elements of a graph is a {\it construction sequence} if no edge is listed before either of its endpoints. The complexity of such a sequence is investigated by finding the delay in placing the edges, an {\it opportunity cost} for the construction sequence. Maximum and minimum cost c-sequences are provided for a variety of graphs and are used to measure the complexity of graph-building programs.