.The intersection power graph of a finite group G is a simple graph whose vertex set is G,in which two distinct vertices and y are adjacent if and only if either one of a and y is the identity element,or(a)n(y)is non-....The intersection power graph of a finite group G is a simple graph whose vertex set is G,in which two distinct vertices and y are adjacent if and only if either one of a and y is the identity element,or(a)n(y)is non-trivial.A number of important graph classes,including cographs,chordal graphs,split graphs,and threshold graphs,can be defined either structurally or in terms of forbidden induced subgraphs.In this paper,we characterize the finite groups whose intersection power graphs are cographs,split graphs,and threshold graphs.We also classify the finite nilpotent groups whose intersection power graphs are chordal.展开更多
基金supported by the National Natural Science Foundation of China(Grant Nos.11801441,61976244)the Natural Science Basic Research Program of Shaanxi(Program No.2020JQ-761)the Shaanxi Fundamental Science Research Project for Mathematics and Physics(Grant No.22JSQ024).
文摘.The intersection power graph of a finite group G is a simple graph whose vertex set is G,in which two distinct vertices and y are adjacent if and only if either one of a and y is the identity element,or(a)n(y)is non-trivial.A number of important graph classes,including cographs,chordal graphs,split graphs,and threshold graphs,can be defined either structurally or in terms of forbidden induced subgraphs.In this paper,we characterize the finite groups whose intersection power graphs are cographs,split graphs,and threshold graphs.We also classify the finite nilpotent groups whose intersection power graphs are chordal.
