Factors in a class of regular digraphs

Abstract For the class of 2‐diregular digraphs: (1) We give a simple closed form expression—a power of 2—for the number of difactors. (2) For the adjacency matrices of these graphs, we show an intimate relationship between the permanent and determinant. (3) We give a necessary and sufficient condition for the Cartesian product of two directed circuits to have a difactor with exactly k components thereby generalizing a result of Trotter and Erdöos. Our results also show that a conjecture of Bondy, regarding vertex‐transitive graphs, fails to hold for vertex‐transitive digraphs.