The orientable genus is determined for any graph that embeds into the projective plane, 2, to be essentially half of the representativity of any embedding into C. In addition, a structure is givenâ€¦ (More)

A graph G is called the 2-amalgamation of subgraphs G, and G2 if G = G, U G, and G, n G, = {x, y), 2 distinct points. In this case we write G = G I U f x , y ) G,. In this paper we show that theâ€¦ (More)

Two underlying propositions, one by Euler and the second a combinatorial observation, can be blamed for a number of conjectures concerning graphs to be embedded or immersed in certain surfaces (i.e.,â€¦ (More)