Classification by girth of three-dimensional algebraically defined monomial graphs over the real numbers

Abstract

For positive integers s, t, u, v, we define a bipartite graph Γ R (X s Y t , X u Y v ) where each partite set is a copy of R 3 , and a vertex (a1, a2, a3) in the first partite set is adjacent to a vertex [x1, x2, x3] in the second partite set if and only ifIn this paper, we classify all such graphs according to girth.