We give a decomposition theorem for Platonic graphs over finite fields and use this to determine the spectrum of these graphs. We also derive estimates for the isoperimetric numbers of the graphs.â€¦ (More)

In this paper we study the integrity of certain graph families. These include planar graphs, graphs with a given genus, graphs on the d-dimensional integer lattice Zd, and graphs that have noâ€¦ (More)

The Platonic graphs Ï€n arise in several contexts, most simply as a quotient of certain Cayley graphs associated to the projective special linear groups. We show that when n = p is prime, Ï€n can beâ€¦ (More)

The Levi graph of a balanced incomplete block design is the bipartite graph whose vertices are the points and blocks of the design, with each block adjacent to those points it contains. We deriveâ€¦ (More)

We obtain formulas for certain weighted sums of values of the symmetric square and triple product L-functions. As a consequence, we get exact values at the right critical point for the symmetricâ€¦ (More)

We derive upper and lower bounds on the isoperimetric numbers and bisection widths of a large class of regular graphs of high degree. Our methods are combinatorial and do not require a knowledge ofâ€¦ (More)

We develop a method for obtaining lower bounds on the Cheeger constants of certain highly connected graphs. We then apply this technique to obtain new lower bounds on the Cheeger constants of twoâ€¦ (More)