Geodesic
Spectra of Boolean Graphs Over Finite Fields of Characteristic Two
Canadian mathematical bulletin, Tome 63 (2020) no. 1, pp. 58-65

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

With entries of the adjacency matrix of a simple graph being regarded as elements of $\mathbb{F}_{2}$, it is proved that a finite commutative ring $R$ with $1\neq 0$is a Boolean ring if and only if either $R\in \{\mathbb{F}_{2},\mathbb{F}_{2}\times \mathbb{F}_{2}\}$ or the eigenvalues (in the algebraic closure of $\mathbb{F}_{2}$) corresponding to the zero-divisor graph of $R$ are precisely the elements of $\mathbb{F}_{4}\setminus \{0\}$ . This is achieved by observing a way in which algebraic behavior in a Boolean ring is encoded within Pascal’s triangle so that computations can be carried out by appealing to classical results from number theory.
DOI : 10.4153/S0008439519000365
Mots-clés : zero-divisor graph, Boolean ring, eigenvalue, Pascal matrix 
Dillery, D. Scott; LaGrange, John D. Spectra of Boolean Graphs Over Finite Fields of Characteristic Two. Canadian mathematical bulletin, Tome 63 (2020) no. 1, pp. 58-65. doi: 10.4153/S0008439519000365
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