On bipartite graphs which attain minimum rank among bipartite graphs with given diameter

Hong-hai Li, Li Su, Hui-xian Sun
2012 The Electronic Journal of Linear Algebra  
Hui-xian. (2012) , "On bipartite graphs which attain minimum rank among bipartite graphs with given diameter", Abstract. The rank of a graph is defined to be the rank of its adjacency matrix. In this paper, the bipartite graphs that attain the minimum rank among bipartite graphs with a given diameter are completely characterized. http://math.technion.ac.il/iic/ela As shown in [9] , there are only finitely many reduced graphs with given rank. Let BG(d) denote the finite set of reduced bipartite
more » ... reduced bipartite graphs with diameter d and rank r(P d+1 ). Note that P d+1 ∈ BG(d). Also, if G has diameter d then G must contain P d+1 as an induced subgraph and so we have r(G) ≥ r(P d+1 ). Hence, BG(d) consists
doi:10.13001/1081-3810.1510 fatcat:iyyifrfp7naj5hofyqs5w67nq4