Year: 2024
Type: article
Abstract: The $Q$-polynomial property is an algebraic property of distance-regular graphs, that was introduced by Delsarte in his study of coding theory. Many distance-regular graphs admit the $Q$-polynomial property. Only recently the $Q$-polynomial property has been generalized to graphs that are not necessarily distance-regular. In [J. Combin. Theory Series. A, 205:105872, 2024] it was shown that the graphs arising from the Hasse diagrams of the so-called attenuated space posets are $Q$-polynomial. These posets could be viewed as $q$-analogs of the Hamming posets, which were not studied in that paper. The main goal of this article is to fill this gap by showing that the graphs arising from the Hasse diagrams of the Hamming posets are $Q$-polynomial.
DOI: 10.37236/12898
Institution: University of Primorska
Language: English
Topic: Finite Group Theory Research
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
Awards: Tree-Independence Number of Graphs, Symmetries in graphs via rigid cells, Terwilliger algebra of a graph, Geometries, Graphs, Groups and their Links, Designing certain discrete mathematical objects in spectral domain, Automorphisms and Isomorphisms of Finite Graphs, Hamilton cycles with rotational symmetry in connected vertex-transitive graphs, Groups, posets, and complexes, Discrete combinatorial objects in the spectral domain - intersection analysis, Algebra, discrete mathematics, probability and game theory
OpenAlex ID: W4403940487