THE NOVI SAD Seminar

 

PROGRAM

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Predavanja možete pratiti i online putem MITEAM stranice Novosadskog seminara:
https://miteam.mi.sanu.ac.rs/asset/3iuT7dhKfDxFv5kh3

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Plan rada Novosadskog seminara za NOVEMBAR 2025

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Utorak, 18.11.2025. u 12:00, svečana sala Ogranka SANU u Novom Sadu, Nikole Pašića 6 i Online
Katarina Žigerović, Matematički institut SANU
THE DIAMETER AND DOMINATING SETS OF THE DIFFERENCE GRAPH OF A NILPOTENT GROUP
Given a group G, the power graph of G is the simple graph whose vertex set is G, such that two vertices are adjacent if one is a power of the other. The enhanced power graph of G is the simple graph with vertex set G, where two vertices are adjacent if they are contained in the same cyclic subgroup.
In 2021, Cameron initiated a study on the differences between these graphs. Given a finite group G, the difference graph of G is defined as the difference between the enhanced power graph and the power graph of G, with all isolated vertices removed.
In this talk, we focus on nilpotent groups and study the graph-theoretic properties of their difference graphs, especially the diameter and domination number. In particular, we prove that the diameter of the difference graph of a nilpotent group has an upper bound of 4. Furthermore, we generalize and refine the result previously obtained by Biswas et al. by classifying all nilpotent groups whose difference graph has diameter k, for each k ≤ 4.
This is joint work with Xuanlong Ma and Samir Zahirović.

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