A description of the Parry-Sullivan number of a graph using circuits
Chris Smith
TL;DR
This paper provides a new way to understand the Parry-Sullivan number of a graph by analyzing its cycles, aiding in the reasoning process for this graph invariant.
Contribution
It introduces a circuit-based description of the Parry-Sullivan number, offering a novel perspective that simplifies its computation and analysis.
Findings
Provides a cycle-based characterization of the Parry-Sullivan number
Facilitates reasoning about the number using graph circuits
Offers a potentially simpler method for calculating the invariant
Abstract
In this short note, we give a description of the Parry-Sullivan number of a graph in terms of the cycles in the graph. This tool is occasionally useful in reasoning about the Parry-Sullivan numbers of graphs.
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Taxonomy
TopicsAdvanced Graph Theory Research · Advanced Graph Theory Research · Complexity and Algorithms in Graphs