Properties of Full-Flag Johnson Graphs
Irving Dai, Michael Greenberg, Noah Schoem, and Matt Tanzer
TL;DR
This paper introduces Full-Flag Johnson graphs, explores their structure as Cayley graphs generated by permutations, and analyzes their adjacency matrices to understand their spectral properties, generalizing permutahedra.
Contribution
It presents the concept of Full-Flag Johnson graphs, establishes their relation to Cayley graphs and permutahedra, and derives spectral results for their adjacency matrices.
Findings
Full-Flag Johnson graphs are Cayley graphs on S_n.
They generalize permutahedra.
Spectral properties of their adjacency matrices are characterized.
Abstract
We introduce and study a variant of the family of Johnson graphs, the Full-Flag Johnson graphs. We show that Full-Flag Johnson graphs are Cayley graphs on S_n generated by certain classes of permutations, and that they are in fact generalizations of permutahedra. We derive some results about the adjacency matrices of Full-Flag Johnson graphs and apply these to the set of permutahedra to deduce part of their spectra.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · graph theory and CDMA systems · Coding theory and cryptography