Queens graphs Original Research Article

The queens graph of a (0,1)-matrix A is the graph whose vertices correspond to the 1ʹs in A and in which two vertices are adjacent if and only if some diagonal or line of A contains the corresponding 1ʹs. A basic question is the determination of which graphs are queens graphs. We establish that a complete block graph is a queens graph if and only if it does not contain K1,5 as an induced subgraph. A similar result is shown to hold for trees and cacti. Every grid graph is shown to be a queens graph, as are the graphs Kn×Pm and C2n×Pm for all integers n,m⩾2. We show that a complete multipartite graph is a queens graph if and only if it is a complete graph or an induced subgraph of K4,4, K1,3,3, K2,2,2 or K1,1,2,2. It is also shown that K3,4−e is not a queens graph.