Compact generalized polygons and Moore graphs as stable graphs

Abstract

We introduce stable graphs as a common generalization of compact generalized polygons with closed adjacency, stable planes and other types of graphs with continuous geometric operations; non-bipartite structures like Moore graphs are also included. Topological and graph-theoretical properties of stable graphs are established, and generalized polygons are characterized among all stable graphs by means of topological properties. Some results about Moore graphs, which might help to find infinite examples, are included.