Institution: | a Department of Computer Science and Engineering, Arizona State University, PO Box 878809, Tempe, AZ 85287-8809, USA b Department of Mathematics, Zhejiang University, Hangzhou 310027, Zhejiang, PR China c Department of Computer Science, University of Vermont, Burlington, VT 05405, USA |
Abstract: | The existence of graph designs for the two nonisomorphic graphs on five vertices and eight edges is determined in the case of index one, with three possible exceptions in total. It is established that for the unique graph with vertex sequence (3, 3, 3, 3, 4), a graph design of order n exists exactly when and n≠16, with the possible exception of n=48. For the unique graph with vertex sequence (2,3,3,4,4), a graph design of order n exists exactly when , with the possible exceptions of n∈{32,48}. |