Enumeration of Point-Determining Graphs

2007/05/01 by Ira M. Gessel, Ira Gessel, Ji Li +2 · 1 citation
Computer Science · Materials Science · Mathematics · #05C30 #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #biodegradable polymer synthesis and properties #math.CO #msc:05C30 #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.0705.0042

26 pages, 11 figures

openalex publication_date 2007/05/01 · arxiv created 2009/11/10 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Complement reducible graphs
• Yoke-Chains and Multipartite Compositions in connexion with the Analytical forms called “Trees”

Cited by

• Unexpectedly, a symmetry on unlabeled graphs

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