Prime graphs and exponential composition of species
Copyright policy )Prime graphs and exponential composition of species
In this paper, we enumerate prime graphs with respect to the Cartesian multiplication of graphs. We use the unique factorization of a connected graph into the product of prime graphs given by Sabidussi to find explicit formulas for labeled and unlabeled prime graphs. In the case of species, we construct the exponential composition of species based on the arithmetic product of species of Maia and Méndez and the quotient species, and express the species of connected graphs as the exponential composition of the species of prime graphs.
30 pages, 7 figures, 1 table
- University of Arizona United States
Species, Exponential composition, Graph operations (line graphs, products, etc.), Exact enumeration problems, generating functions, species, arithmetic product, Prime graphs, Arithmetic product, Enumeration in graph theory, Graphs and abstract algebra (groups, rings, fields, etc.), Theoretical Computer Science, Computational Theory and Mathematics, Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.), prime graphs, Cartesian product, FOS: Mathematics, Discrete Mathematics and Combinatorics, Mathematics - Combinatorics, 05C30, Combinatorics (math.CO), exponential composition
Species, Exponential composition, Graph operations (line graphs, products, etc.), Exact enumeration problems, generating functions, species, arithmetic product, Prime graphs, Arithmetic product, Enumeration in graph theory, Graphs and abstract algebra (groups, rings, fields, etc.), Theoretical Computer Science, Computational Theory and Mathematics, Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.), prime graphs, Cartesian product, FOS: Mathematics, Discrete Mathematics and Combinatorics, Mathematics - Combinatorics, 05C30, Combinatorics (math.CO), exponential composition
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