Details

Autor(en) / Beteiligte

• Dillery, D. Scott
• LaGrange, John D.

Titel

Spectra of Boolean Graphs Over Finite Fields of Characteristic Two

Ist Teil von

• Canadian mathematical bulletin, 2020-03, Vol.63 (1), p.58-65

Ort / Verlag

Montreal: Cambridge University Press

Erscheinungsjahr

2020

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• Abstract 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.