Base graph–connection graph: Dissection and construction

This paper presents a phenomenon which sometimes occurs in tetravalent bipartite locally dart-transitive graphs, called Base Graph–Connection Graph dissection. In this dissection, each white vertex is split into two vertices of valence 2 so that the connected components result are isomorphic. Given whose subdivision isomorphic to component, and Connection Graph, describes how overlap, we can, some cases, provide construction can make graph having such decomposition. investigates general as well special cases connection has no more than one edge.