For a group G and a non-empty subsetΩof G,the commuting graph C(G,Ω)ofΩis a graph whose vertex set isΩand any two vertices are adjacent if and only if they commute in G.Define T4n=(a,b|a^(2)n=b^(4)=1,an=b2,b^(−1)a...For a group G and a non-empty subsetΩof G,the commuting graph C(G,Ω)ofΩis a graph whose vertex set isΩand any two vertices are adjacent if and only if they commute in G.Define T4n=(a,b|a^(2)n=b^(4)=1,an=b2,b^(−1)ab=a^(−1)),the dicyclic group of order 4n(n≥3),which is also known as the generalized quaternion group.We mainly investigate the properties and metric dimension of the commuting graphs on the dicyclic group T4n.展开更多
基金This work was supported by NSFC Grant 11871206Natural Science Foundation of Hunan Province(No.2020JJ4233,No.2020JJ5096).
文摘For a group G and a non-empty subsetΩof G,the commuting graph C(G,Ω)ofΩis a graph whose vertex set isΩand any two vertices are adjacent if and only if they commute in G.Define T4n=(a,b|a^(2)n=b^(4)=1,an=b2,b^(−1)ab=a^(−1)),the dicyclic group of order 4n(n≥3),which is also known as the generalized quaternion group.We mainly investigate the properties and metric dimension of the commuting graphs on the dicyclic group T4n.
