×

Index of imprimitivity of the non-complete extended \(p\)-sum of digraphs. (English) Zbl 0941.05043

The greatest common divisor of the lengths of all cycles of a digraph is called the index of imprimitivity of the digraph. The author proves that all components of the non-complete extended \(p\)-sum of strongly connected digraphs have the same index of imprimitivity and expresses it in terms of the imprimitivity indices of the digraphs on which the operation is performed. Spectral techniques are used.

MSC:

05C50 Graphs and linear algebra (matrices, eigenvalues, etc.)
05C20 Directed graphs (digraphs), tournaments