Geodesic
On linear transformations preserving cyclicity index of nonnegative matrices
Fundamentalʹnaâ i prikladnaâ matematika, Tome 25 (2024) no. 1, pp. 67-82

Voir la notice de l'article provenant de la source Math-Net.Ru

The cyclicity index of a strongly connected directed graph is the greatest common divisor of all its directed cycles and the cyclicity index of an arbitrary directed graph is the least common multiple of the cyclicity indices of all its maximal strongly connected subgraphs. The cyclicity index of a matrix is equal to the cyclicity index of its critical subgraph, namely, the subgraph of the adjacent graph consisting of all cycles with the maximal average weight. In this paper, we consider surjective linear transformations of non-negative and integer non-negative matrices preserving the cyclicity index. We obtain a complete characterization of such maps and prove that they are automatically injective. 
@article{FPM_2024_25_1_a3,
     author = {A. V. Vlasov and A. E. Guterman and E. M. Kreines},
     title = {On linear transformations preserving cyclicity index of nonnegative matrices},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {67--82},
     publisher = {mathdoc},
     volume = {25},
     number = {1},
     year = {2024},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2024_25_1_a3/}
}
TY  - JOUR
AU  - A. V. Vlasov
AU  - A. E. Guterman
AU  - E. M. Kreines
TI  - On linear transformations preserving cyclicity index of nonnegative matrices
JO  - Fundamentalʹnaâ i prikladnaâ matematika
PY  - 2024
SP  - 67
EP  - 82
VL  - 25
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/FPM_2024_25_1_a3/
LA  - ru
ID  - FPM_2024_25_1_a3
ER  - 
%0 Journal Article
%A A. V. Vlasov
%A A. E. Guterman
%A E. M. Kreines
%T On linear transformations preserving cyclicity index of nonnegative matrices
%J Fundamentalʹnaâ i prikladnaâ matematika
%D 2024
%P 67-82
%V 25
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/FPM_2024_25_1_a3/
%G ru
%F FPM_2024_25_1_a3
A. V. Vlasov; A. E. Guterman; E. M. Kreines. On linear transformations preserving cyclicity index of nonnegative matrices. Fundamentalʹnaâ i prikladnaâ matematika, Tome 25 (2024) no. 1, pp. 67-82. http://geodesic.mathdoc.fr/item/FPM_2024_25_1_a3/