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31 papers · 1 filter
The Terwilliger algebras of doubly regular tournaments
Allen Herman
The Terwilliger algebras of asymmetric association schemes of rank , whose nonidentity relations correspond to doubly regular tournaments, are shown to have thin irreducible mod…
Induced forests in some distance-regular graphs
Karen Gunderson, Karen Meagher, Joy Morris +1
In this article, we study the order and structure of the largest induced forests in some families of graphs. First we prove a variation of the ratio bound that gives an upper bound…
Sparsity of Graphs that Allow Two Distinct Eigenvalues
Wayne Barrett, Shaun Fallat, Veronika Furst +5
The parameter of a graph is the minimum number of distinct eigenvalues over the family of symmetric matrices described by . It is shown that the minimum number of edg…
On non-normal subgroup perfect codes
Angelot Behajaina, Roghayeh Maleki, Andriaherimanana Sarobidy Razafimahatratra
Let be a graph. A subset is a \emph{perfect code} of if is a coclique of with the property that any vertex in is adjace…
On multipartite derangement graphs
Andriaherimanana Sarobidy Razafimahatratra
Given a finite transitive permutation group , with , the derangement graph of is the Cayley graph $\operatorname{Cay}(G,\operatorn…
Complex Hadamard Diagonalisable Graphs
Ada Chan, Shaun Fallat, Steve Kirkland +3
In light of recent interest in Hadamard diagonalisable graphs (graphs whose Laplacian matrix is diagonalisable by a Hadamard matrix), we generalise this notion from real to complex…