On the Component Number of Links from Plane Graphs
Daniel S. Silver, Susan G. Williams
TL;DR
This paper provides a simple proof connecting the number of link components from a medial graph to the nullity of the mod-2 Laplacian matrix of the original graph.
Contribution
It offers an elementary proof of a relationship between link components and graph Laplacian nullity, clarifying a key topological-graph theoretical connection.
Findings
Number of link components equals nullity of mod-2 Laplacian
Elementary proof of the relationship
Clarifies link between graph topology and algebraic invariants
Abstract
A short, elementary proof is given of the result: The number of components of a link arising from a medial graph M(G) by resolving vertices is equal to the nullity of the mod-2 Laplacian matrix of the graph G.
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