Enumeration of Point-Determining Graphs

TL;DR

This paper uses combinatorial species theory to enumerate various classes of point-determining graphs, including their connected and bicolored variants, providing a comprehensive combinatorial analysis.

Contribution

It introduces a systematic enumeration of point-determining, co-point-determining, bi-point-determining, and bicolored point-determining graphs using species theory.

Findings

Enumeration formulas for each graph class

Results on connected point-determining graphs

Analysis of bicolored point-determining graphs

Abstract

Point-determining graphs are graphs in which no two vertices have the same neighborhoods, co-point-determining graphs are those whose complements are point-determining, and bi-point-determining graphs are those both point-determining and co-point-determining. Bicolored point-determining graphs are point-determining graphs whose vertices are properly colored with white and black. We use the combinatorial theory of species to enumerate these graphs as well as the connected cases.