FEDRIANI , E.m.

There are many problems in Graph Theory for finite graphs relating the number of vertices and the number of edges and, therefore, related to the average degree for finite graphs. However, when dealing with real-life problems involving networks, it is often useful to model the situation by using infinite graphs, which can represent extendable...

Chartrand and Harary characterized finite outer-planar graphs, and Wagner studied uncountable graphs admitting a planar embedding. We continue this research for those outer-S graphs in surfaces S by studying un countable graphs admitting S-embeddings with all their vertices in the same face (namely, outer-S embeddings).

In this paper, we describe a new method to classify complex filiform Lie algebras based on the concept of isomorphism between Lie algebras. This method, which has the advantage of being applied to any dimension, gives the families of algebras in each dimension in an explicit way. In order to apply, only the corresponding structure the- orem of...