@article{Cui2026, 
author = {Chunqiang Cui and Changliang Wang},
title = {Notes on the equitable graph of type II of a finite group},
year = {2026},
journal = {Electronic Research Archive},
volume = {34},
number = {3},
pages = {2087-2098},
keywords = {equitable graph of type II, finite group, metric dimension},
url = {https://www.sciopen.com/article/10.3934/era.2026093},
doi = {10.3934/era.2026093},
abstract = {Given a finite group    G, the equitable graph of type II defined on    G is an undirected graph with vertex set    G, in which two distinct vertices    a and    b are adjacent if and only if either    0  <      |    o  (  a  )  −  o  (  b  )      |    ≤  min  {  o  (  a  )  ,  o  (  b  )  } or one of    a and    b is equal to    e, where    o  (  a  ) and    o  (  b  ) are the orders of    a and    b, respectively. In this paper, we observe that every equitable graph of type II of a finite group is a generalized lexicographic product and discuss finite groups    G whose equitable graph of type II is        C    n  -free, where    n  ≥  3. As an application, we show that every equitable graph of type II of a finite group is perfect. Finally, we characterize the metric dimension of the equitable graph of type II of a finite group.}
}