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A Note on p-Cyclic Matrices and Digraphs

Published online by Cambridge University Press:  20 November 2018

B. R. Heap  and
M. S Lynn
B. R. Heap
Affiliation:
Mathematics Division, National Physical Laboratory, Teddington, Middlesex, England
M. S Lynn
Affiliation:
IBM Scientific Centre, 6900 Fannin, Houston, Texas 77025
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We use the terminology of [1]. Let D be a strongly connected digraph on n points and containing m lines, and let A = A(D) be the corresponding adjacency matrix, so that A is an n x n 0-1 matrix containing m unit elements. We recall that A and D are said to be p-cyclic if p is the greatest common divisor of the lengths of all directed cycles of D. Clearly, the larger the value of p, the smaller the value of m must be; in this note we make the latter and related statements precise.

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 10 , Issue 4 , October 1967 , pp. 497 - 501
Copyright
Copyright © Canadian Mathematical Society 1967

References

1. Harary, F., Norman, R. Z. and Cartwright, D.: Structural models: an introduction to the theory of directed graphs, Wiley, New, 1965.Google Scholar