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A Class of Normal (0, 1)-Matrices

Published online by Cambridge University Press:  20 November 2018

W. G. Bridges*
Affiliation:
University of Wyoming, Laramie, Wyoming
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If A is a real normal matrix At (the transpose of A) is a real polynomial in A. We study here those normal (0, 1)-matrices A with constant row sums which have At a polynomial of degree two in A.

Type
Research Article
Copyright
Copyright © Canadian Mathematical Society 1973

References

1. Bridges, W. G., The polynomial of a non-regular digraph, Pacific J. Math. 38 (1971), 325342.Google Scholar
2. Hall, M., Jr., Combinatorial theory (Blaisdell, Waltham, Mass., 1967).Google Scholar
3. Hoffman, A. J., On the polynomial of a graph, Amer. Math. Monthly 70 (1963), 3036.Google Scholar
4. Hoffman, A. J. and McAndrew, M. H., On the polynomial of a directed graph, Proc. Amer. Math. Soc. 10 (1965), 303309.Google Scholar
5. Hoffman, A. J. and Singleton, R. R., On Moore graphs of diameter 2 and 3, IBM J. Res. Develop. 4 (1960), 497504.Google Scholar
6. Ryser, H. J., A generalization of the matrix equation A2 = J, Linear Algebra and Appl. 3 (1970), 451460.Google Scholar
7. Seidel, J. J., Strongly regular graphs with ( — 1, 1, 0) adjacency matrix having eigenvalue 3, Linear Algebra and Appl. 1 (1968), 281298.Google Scholar