(SI) V tem projektu bomo študirali graf $Gamma=(X,R)$ z $d+1$ različnih lastnih vrednosti, za katere algebra matrik generirana s primitivnim idempotentoma ${E_0, E_1, …, E_d}$ ima drugo bazo sestavljeno iz ničelnih $|X|times|X|$ $(0,1)$-matrik ${F_0, F=F_1,…,F_d}$. Rezultati projekta bodo predstavljeni na mednarodnih konferencah (Evropski matematični kongres 2020 v Portorožu) in seminarjih ter objavljeni v uglednih mednarodnih revijah z velikim faktorjem vpliva.
(EN) In this project we study the graph $Gamma=(X,R)$ with $d+1$ distinct eigenvalues for which the algebra of matrices generated by the primitive idempotents ${E_0, E_1, …, E_d}$ has a second basis consisting of zero $|X|times|X|$ $(0,1)$-matrices ${F_0, F=F_1,…,F_d}$. The results of the project will be presented at international conferences (European Mathematical Congress 2020 in Portorož) and seminars and published in reputable international journals with high impact factors.