The first section, Sec. 3.1, is the more important one for this chapter. It defines the various ranks of connectedness for transfinite graphs, presents the critical Condition 3.1-2 that insures that connectedness is transitive, and shows how at each rank this partitions a transfinite graph into nonoverlapping subgraphs, called “sections.” Sec. 3.2 explains how a transfinite tree can be easily contracted to and expanded from a conventional tree. Sec. 3.3 relates the v-nodes and (y-1)-sections of a v-graph to a hypergraph and gives an example of how a result from hypergraph theory can be transferred to transfinite graph theory.
KeywordsInternal Node Terminal Node Boundary Node Large Circle Sequential Representation
Unable to display preview. Download preview PDF.