More on the Second Babai Number and Second Clique Number of Q~3

摘要

In this paper, we look at the second Babai number and second clique number of the three-dimensional rational space Q~3, denoted B_2(Q~3) and C_2(Q~3) respectively. It is shown that C_2(Q~3) = 6 and B_2(Q~3) ≥ 6, an improvement of the bounds given by Johnson and Tiemeyer in [6]. We conclude by showing exactly which Euclidean distance graphs with two adjacency distances and vertex set Q~3 have clique number 6.