Jason Williford

New families of Q-polynomial association schemes

In this paper, we construct the first known infinite family of primitive Q-polynomial schemes which are not generated by distance-regular graphs. To construct these examples, we introduce the notion of a relative hemisystem of a generalized quadrangle with respect to a subquadrangle.

On the Wiener index, distance cospectrality and transmission-regular graphs

In this paper, we investigate various algebraic and graph theoretic properties of the distance matrix of a graph. Two graphs are

Double covers of symplectic dual polar graphs

D

Graphs without theta subgraphs

-cospectral if their distance matrices have the same spectrum. We construct infinite pairs of

The eigenvalues of the graphs D(4,q)

D

Imprimitive cometric association schemes: Constructions and analysis

-cospectral graphs with different diameter and different Wiener index. A graph is

On monomial graphs of girth eight

k

Extremal graphs without 4-cycles

-transmission-regular if its distance matrix has constant row sum equal to

There are finitely many Q-polynomial association schemes with given first multiplicity at least three

k

The independence number for polarity graphs of even order planes

. We establish tight upper and lower bounds for the row sum of a