5 papers · 1 filter
Near-factorizations in association schemes
Allen Herman, Alice Lacaze-Masmonteil, Karen Meagher +1
We formally initiate the study of -fold near-factorizations in association schemes. Namely, given an association , we consider the existence of a facto…
On Matrix Product Factorization in Association Schemes
Allen W. Herman, Bobby Miraftab
We study matrix product factorizations (MPFs) in symmetric association schemes: identities where are loopless unions of basic relations and the ordinary…
On Matrix Product Factorization of Cayley graphs
Allen W. Herman, Bobby Miraftab
We study when the adjacency matrix of a Cayley graph factors as the product of two adjacency matrices of Cayley graphs. Let be a finite group and let $U\subseteq G\setminus \{e…
On the second largest eigenvalue of certain graphs in the perfect matching association scheme
Himanshu Gupta, Allen Herman, Alice Lacaze-Masmonteil +2
The perfect matching association scheme is a set of relations on the perfect matchings of the complete graph on vertices. The relations between perfect matchings are defined b…
Minimum number of distinct eigenvalues of distance-regular and signed Johnson graphs
Shaun Fallat, Himanshu Gupta, Allen Herman +1
We study the minimum number of distinct eigenvalues over a collection of matrices associated with a graph. Lower bounds are derived based on the existence or non-existence of certa…