Descending endomorphism graphs of groups

Document Type

Article

Publication Title

AKCE International Journal of Graphs and Combinatorics

Abstract

We define a new type of graph of a group with reference to the descending endomorphisms of the group. A descending endomorphism of a group is an endomorphism that induces a corresponding endomorphism in every homomorphic image of the group. We define the undirected (directed) descending endomorphism graph of a group as the undirected (directed) graph whose vertex set is the underlying set of the group, in which there is an undirected (directed) edge from one vertex to another if the group has a descending endomorphism that maps the former element to the latter. We investigate some basic properties of these graphs and show that they are closely related to power graphs. We also determine the descending endomorphism graphs of symmetric, dihedral, and dicyclic groups.

First Page

148

Last Page

155

DOI

10.1080/09728600.2023.2234956

Publication Date

1-1-2023

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