Graphical Compositions 1: Basic Enumeration
A Knopfmacher, M E Mays
TL;DR
This paper explores the enumeration of graph compositions, providing formulas, generating functions, and recurrence relations for counting compositions across various graph families, thereby extending understanding of graph-based combinatorial structures.
Contribution
It introduces new formulas and recurrence relations for counting graph compositions in multiple graph families, advancing combinatorial enumeration methods.
Findings
Derived formulas for graph composition counts
Established generating functions for various graph families
Presented recurrence relations for enumeration
Abstract
Graph compositions generalize both integer compositions and partitions of a finite set. We develop formulas, generating functions and recurrence relations for composition counting functions for several families of graphs.
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Taxonomy
TopicsHistory and advancements in chemistry · Advanced Combinatorial Mathematics · Graph theory and applications