We introduce and investigate the concept of Queen labeling a digraph and its connection to the well-known n-queens problem. In the
general case we obtain an upper bound on the size of a queen graph and show that it is tight. We also examine the existence of possible forbid-den subgraphs for this problem and show that only two such subgraphs
exist. Then we focus on specific graph families: First we show that every
star is a queen graph by giving an algorithm for which we prove cor-rectness. Then we show that the problem of queen labeling a matching is equivalent to a variation of the n-queens problem, which we call the
rooks-and-queens problem and we use that fact to give a short proof that every matching is a queen graph. Finally, for unions of 3-cycles we give a general solution of the problem for graphs of n(n - 1) vertices.
All rights reserved. This work is protected by the corresponding intellectual and industrial property rights. Without prejudice to any existing legal exemptions, reproduction, distribution, public communication or transformation of this work are prohibited without permission of the copyright holder. If you wish to make any use of the work not provided for in the law, please contact: firstname.lastname@example.org