Research Communication | Open Access
Volume 2021 | Communication ID 263
Volume 2021 | Communication ID 263
| The idiosyncratic polynomial of digraphs |
Edward Bankoussou-Mabiala, Abderrahim Boussaïri, Abdelhak Chaïchaâ, Brahim Chergui, Soufiane Lakhlifi
Received |
Accepted |
Published |
January 31, 2021 |
February 15, 2021 |
March 15, 2021 |
Abstract: The idiosyncratic polynomial of a graph $G$ with adjacency matrix $A$ is the characteristic polynomial of the matrix $ A + y(J-A-I)$, where $I$ is the identity matrix and $J$ is the all-ones matrix. It follows from a theorem of Hagos (2000) combined with an earlier result of Johnson and Newman (1980) that the idiosyncratic polynomial of a graph is reconstructible from the multiset of the idiosyncratic polynomial of its vertex-deleted subgraphs. For a digraph $G$ with adjacency matrix $A$, we define its idiosyncratic polynomial as the characteristic polynomial of the matrix $ A + ...