Lindsay Marjanski ; Vincent Solon ; Frank Zheng ; Kathleen Zopff - Geodesic Growth of Numbered Graph Products

gcc:10019 - journal of Groups, complexity, cryptology, February 4, 2023, Volume 14, Issue 2 - https://doi.org/10.46298/jgcc.2023.14.2.10019
Geodesic Growth of Numbered Graph ProductsArticle

Authors: Lindsay Marjanski ; Eden Solon ; Frank Zheng ; Kathleen Zopff

    In this paper, we study geodesic growth of numbered graph products; these are a generalization of right-angled Coxeter groups, defined as graph products of finite cyclic groups. We first define a graph-theoretic condition called link-regularity, as well as a natural equivalence amongst link-regular numbered graphs, and show that numbered graph products associated to link-regular numbered graphs must have the same geodesic growth series. Next, we derive a formula for the geodesic growth of right-angled Coxeter groups associated to link-regular graphs. Finally, we find a system of equations that can be used to solve for the geodesic growth of numbered graph products corresponding to link-regular numbered graphs that contain no triangles and have constant vertex numbering.


    Volume: Volume 14, Issue 2
    Published on: February 4, 2023
    Accepted on: January 25, 2023
    Submitted on: September 8, 2022
    Keywords: Mathematics - Combinatorics,Mathematics - Group Theory,20F55, 05A15, 20F10

    Consultation statistics

    This page has been seen 1249 times.
    This article's PDF has been downloaded 654 times.