Descending endomorphism graphs of groups

Vinay Madhusudanan, G. Sudhakara, Arjit Seth

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish
Pages (from-to)148-155
Number of pages8
JournalAKCE International Journal of Graphs and Combinatorics
Issue number2
Publication statusAccepted/In press - 2023

All Science Journal Classification (ASJC) codes

  • Discrete Mathematics and Combinatorics


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