Geodesic
The Exponents of Strongly Connected Graphs
Canadian journal of mathematics, Tome 21 (1969) no. 1, pp. 769-782

Voir la notice de l'article provenant de la source Cambridge University Press

A directed graphG is a set of vertices V and a subset of V × V called the edges of G. A path in G of length k, is such that (vi, vi+1) is an edge of G for 1 ≦ i ≦ k. A directed graph G is strongly connected if there is a path from every vertex of G to every other vertex. A circuit is a path whose two end vertices are equal. An elementary circuit has no other equal vertices. See (1) for a fuller discussion.Let G be a finite, strongly connected, directed graph (fscdg). The kth power Gk of G is the directed graph with the same vertices as G and edges of the form (i, j) where G has a path of length k from i to j. 
Bender, Edward A.; Tucker, Thomas W. The Exponents of Strongly Connected Graphs. Canadian journal of mathematics, Tome 21 (1969) no. 1, pp. 769-782. doi: 10.4153/CJM-1969-088-3
@article{10_4153_CJM_1969_088_3,
     author = {Bender, Edward A. and Tucker, Thomas W.},
     title = {The {Exponents} of {Strongly} {Connected} {Graphs}},
     journal = {Canadian journal of mathematics},
     pages = {769--782},
     year = {1969},
     volume = {21},
     number = {1},
     doi = {10.4153/CJM-1969-088-3},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CJM-1969-088-3/}
}
TY  - JOUR
AU  - Bender, Edward A.
AU  - Tucker, Thomas W.
TI  - The Exponents of Strongly Connected Graphs
JO  - Canadian journal of mathematics
PY  - 1969
SP  - 769
EP  - 782
VL  - 21
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.4153/CJM-1969-088-3/
DO  - 10.4153/CJM-1969-088-3
ID  - 10_4153_CJM_1969_088_3
ER  - 
%0 Journal Article
%A Bender, Edward A.
%A Tucker, Thomas W.
%T The Exponents of Strongly Connected Graphs
%J Canadian journal of mathematics
%D 1969
%P 769-782
%V 21
%N 1
%U http://geodesic.mathdoc.fr/articles/10.4153/CJM-1969-088-3/
%R 10.4153/CJM-1969-088-3
%F 10_4153_CJM_1969_088_3

[1] 1. Berge, C., The theory of graphs and its applications (Wiley, New York, 1962). Google Scholar

[2] 2. Brauer, A. and Schockley, J. E., On a problem of Frobenius, J. Reine Angew. Math. 211 (1962), 215–220. Google Scholar

[3] 3. Dulmage, A. L. and Mendelsohn, N. S., Gaps in the exponent set of primitive matrices, Illinois J. Math. 8 (1964), 642–656. Google Scholar

[4] 4. Heap, B. R. and Lynn, M. S., The structure of powers of non-negative matrices. I. The index of convergence (National Physical Laboratory, Teddington, Middlesex, England, 1964), SIAM J. Appl. Math. 14 (1966), 610–639. Google Scholar

[5] 5. Norman, R. Z., private communication. Google Scholar

[6] 6. Ptâk, V. and Sedlâcek, J., On the index of imprimitivity of non-negative matrices, Czechoslovak Math. J. 8 (83) (1958), 496–501. Google Scholar

[7] 7. Roberts, J. B., Note on linear forms, Proc. Amer. Math. Soc. 7 (1956), 465–469. Google Scholar

[8] 8. Tucker, T. W., The exponent set of strongly connected graphs, Senior thesis, Harvard University, 1967. Google Scholar

[9] 9. Wielandt, H., Unzerlegbare, nicht negativen Matrizen, Math. Z. 52 (1950), 642–648. Google Scholar

Cité par Sources :