The Commuting Graphs on Dicyclic Groups

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.