2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/171809We study characteristics which might distinguish two-graphs by introducing different numerical measures on the collection of graphs on $n$ vertices. Two conjectures are stated, one using these numerical measures and the other using the deck of a graph, which suggest that there is a finite set of conditions differentiating two-graphs. We verify that, among the four non-trivial non-isomorphic regular two-graphs on 26 vertices, both conjectures hold.15 pages, accepted by the Rocky Mountain Journal of MathematicsCombinatoricsFunctional Analysis05C50;42C15text