Enumeration of Point-Determining Graphs
Ira Gessel, Ji Li

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.
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Taxonomy
TopicsAdvanced Graph Theory Research · semigroups and automata theory · biodegradable polymer synthesis and properties
