Faculty Research Mentor: Michelle Robinette, Ph.D.1
1College of Sciences, Department of Mathematical Sciences
A graph is a collection of vertices, sometimes called nodes, along with edges, which are lines joining the vertices. By using a procedure called the line graph procedure, we can use a graph G to form a new graph called the line graph of G, or L(G). The procedure forms L(G) by using the edges of G as the vertices of L(G), and by having two vertices in L(G) have an edge joining them if these vertices, as edges, share a vertex in G. The line graph is the simplest graph procedure in a collection of procedures called the H-line graph procedures. In this article, I investigate the properties of the iterated H-line graph procedure, i.e. when the procedure is applied multiple times to the same graph. In particular, I find families of graphs whose iterated H-line graph procedure creates graphs that grow indefinitely in number of vertices. Furthermore, I use these families to find the properties of graphs whose iterated H-line graph procedure produces the same graph after enough iterations.