Jesus Arturo Jimenez Gonzalez - A graph theoretical framework for the strong Gram classification of non-negative unit forms of Dynkin type A

fi:7596 - Fundamenta Informaticae, December 23, 2021, Volume 184, Issue 1
A graph theoretical framework for the strong Gram classification of non-negative unit forms of Dynkin type A

Authors: Jesus Arturo Jimenez Gonzalez

    In the context of signed line graphs, this article introduces a modified inflation technique to study strong Gram congruence of non-negative (integral quadratic) unit forms, and uses it to show that weak and strong Gram congruence coincide among positive unit forms of Dynkin type A. The concept of inverse of a quiver is also introduced, and is used to obtain and analyze the Coxeter matrix of non-negative unit forms of Dynkin type A. Connected principal unit forms of such type are also classified.


    Volume: Volume 184, Issue 1
    Published on: December 23, 2021
    Accepted on: November 16, 2021
    Submitted on: June 16, 2021
    Keywords: Mathematics - Combinatorics,15A63, 15A21, 15B36, 05C22, 05C50, 05C76, 05B20

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