Title: Short note about commutative association schemes and specific (directed) family of graphs
| Speaker: | Safet Penjić |
| Affiliation: | University of Primorska |
| Location: | Please contact Sabrina Lato for Zoom link |
Abstract: In this talk, we consider the following problem:
{\bf Problem.} When the Bose--Mesner algebra ${\cal M}$ of commutative $d$-class association scheme ${\mathfrak X}$ (which is not necessarily symmetric) can be generated by a $01$-matrix $A$? With other words, for a given ${\mathfrak X}$ can we find $01$-matrix $A$ such that ${\cal M}=(\langle A\rangle, +, \cdot)$? Moreover, since such a matrix $A$ is the adjacency matrix of some (un)directed graph $\Gamma$, can we describe the combinatorial structure of $\Gamma$? Vice-versa question is also of importance, i.e., what combinatorial structure does (un)directed graph need to have so that its adjacency matrix will generate the Bose-Mesner algebra of a commutative $d$-class association scheme ${\mathfrak X}$?