Jongyook Park

TL;DR: It is shown that there are finitely many Shilla distance-regular graphs @C with fixed b(@C)>=2 and b( @C)=3, and a new existence condition for distance- regular graphs, in general is given.

TL;DR: In this paper, it was shown that there are finitely many Shilla distance-regular graphs G with fixed b(G)>=2 and fixed b=b(G):=k/a3.

TL;DR: It is shown that if the diameter is at least three, then such a graph, besides a finite number of exceptions, is a Taylor graph, bipartite with diameter three or a line graph.

TL;DR: For a distance-regular graph with second largest eigenvalue θ 1 (resp., smallest eigen value) θ D, it was shown in this article that (θ 1 + 1 )(θ D + 1 + b 1 ) ⩽ - b 1 holds, where equality only holds when the diameter equals two.

TL;DR: In this paper, it was shown that if the distance between points is measured by electric resistance then all points are close to being equidistant on a distance-regular graph with large valency, and that the ratio between resistances between pairs of vertices in a distance regular graph of diameter 3 or more is bounded by 1+6k, where k is the degree of the graph.