A characterization of bipartite distance-regular graphs

Abstract

It is well-known that the halved graphs of a bipartite distanceregular graph are distance-regular. Examples are given to show that the converse does not hold. Thus, a natural question is to find out when the converse is true. In this paper we give a quasi-spectral characterization of a connected bipartite weighted 2-punctually distance-regular graph whose halved graphs are distance-regular. In the case the spectral diameter is even we show that the graph characterized above is distanceregular. (C) 2013 Elsevier Inc. All rights reserved.