We investigate the behavior of electric potentials on distance-regular graphs, and extend some results of a prior paper, [12]. Our main result, Theorem 4 below, shows(together with Corollary 3) thatâ€¦ (More)

A Shilla distance-regular graph Î“ (say with valency k) is a distance-regular graph with diameter 3 such that its second largest eigenvalue equals to a3. We will show that a3 divides k for a Shillaâ€¦ (More)

In this paper we will look at the relationship between the intersection number c2 and its diameter for a distance-regular graph. And also, we give some tools to show that a distance-regular graphâ€¦ (More)

Godsil showed that if Î“ is a distance-regular graph with diameter D > 3 and valency k > 3, and Î¸ is an eigenvalue of Î“ with multiplicity m > 2, then k 6 (m+2)(mâˆ’1) 2 . In this paper we will give aâ€¦ (More)

In this paper, we show that for given positive integer C, there are only finitely many distance-regular graphs with valency k at least three, diameter D at least six and k2 k â‰¤ C. This extends aâ€¦ (More)

In 1986, Terwilliger showed that there is a strong relation between the eigenvalues of a distance-regular graph and the eigenvalues of a local graph. In particular, he showed that the eigenvalues ofâ€¦ (More)

In this talk we study distance-regular graphs with a small number of vertices compared to the valency. We show that for a given Î± > 2, there are finitely many distance-regular graphs Î“ with valencyâ€¦ (More)