A Note on Constructing Large Cayley Graphs of Given Degree and Diameter by Voltage Assignments

Voltage graphs are a powerful tool for constructing large graphs (called lifts) with prescribed properties as covering spaces of small base graphs. This makes them suitable for application to the degree/diameter problem, which is to determine the largest order of a graph with given degree and diameter. Many currently known largest graphs of degree ≤ 15 and diameter ≤ 10 have been found by computer search among Cayley graphs of semidirect products of cyclic groups. We show that all of them can in fact be described as lifts of smaller Cayley graphs of cyclic groups, with voltages in (other) cyclic groups. ∗ This research started when J. Plesn´ık and J. ˇSir´aˇn were visiting the Department of Computer Science and Software Engineering of the University of Newcastle NSW Australia in 1995, supported by small ARC grant. 1 

• Type: Journal
• Year: 1998
• Where: COMBINATORICS
• Authors: Ljiljana Brankovic, Mirka Miller, Ján Plesník, Joseph F. Ryan, Jozef Sirán
• Keywords: Cayley Graphs, COMBINATORICS 1998, Cyclic Groups, Small Base Graphs