Open AccessBook Embeddings of Infinite Sequences of Extended Periodic Regular Graphs
Author(s) -
Benny Pitoan,
Jullia Titaley
Publication year - 2019
Publication title -
iop conference series. materials science and engineering
Language(s) - English
Resource type - Journals
eISSN - 1757-899X
pISSN - 1757-8981
DOI - 10.1088/1757-899x/621/1/012011
Subject(s) - combinatorics , embedding , mathematics , graph , discrete mathematics , book embedding , sequence (biology) , line graph , 1 planar graph , computer science , artificial intelligence , biology , genetics
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.