Statistics on Small Graphs
Richard J. Mathar

TL;DR
This paper systematically catalogs small graphs with up to 10 edges and vertices, classifying them by various properties and providing comprehensive counts for each category.
Contribution
It offers the first detailed enumeration and classification tables for small graphs based on multiple standard properties.
Findings
Tables of graph counts in various categories
Classification of small graphs by multiple properties
Comprehensive enumeration data
Abstract
We create the unlabeled or vertex-labeled graphs with up to 10 edges and up to 10 vertices and classify them by a set of standard properties: directed or not, vertex-labeled or not, connectivity, presence of isolated vertices, presence of multiedges and presence of loops. We present tables of how many graphs exist in these categories.
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Taxonomy
TopicsGraph Labeling and Dimension Problems · Advanced Graph Theory Research · Data Management and Algorithms
