Abstract
The queens graph of a (0,1)-matrix A is the graph whose vertices correspond to the 1's in A and in which two vertices are adjacent if and only if some diagonal or line of A contains the corresponding 1's. 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 K 1,5 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 K n × P m and C 2 n × P m 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 K 4,4, K 1,3,3, K 2,2,2 or K 1,1,2,2. It is also shown that K 3,4− e is not a queens graph.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
