The Chords of the Non-Ruled Quadric In PG (3, 3)
W. T. Tutte · Canadian Journal of Mathematics · 1958
The 8-cage (3) may be defined as the simplest cubic graph having no circuit of fewer than eight edges. To construct it we first observe that it must contain a tree T whose vertices are of degrees 1 and 3 and in which each vertex of degree 1 is separated by an arc of just three edges from a central edge AB . These properties fix the structure of T uniquely.