Book Embeddings of Infinite Sequences of Extended Periodic Regular Graphs

A graph is extended periodic if it can be made up by gluing identical pieces together with a graph which is isomorphic to or subgraph of that piece, in a circular fashion. We consider an infinite sequence H n of extended periodic 4-regular graphs and an infinite sequence M n of extended periodic 5-regular graphs. A book is a collection of half-planes called pages, all having a common boundary called the spine. A book embedding of a graph G is to put the vertices of G on the spine and each edge of G is contained in one page. The minimum pages needed to embed a graph G into a book is called pagenumber of G . We determine the pagenumbers of H n and M n to be three.