Distance-regular graphs with an eigenvalue -k %26lt; theta %26lt;= 2-k

作者：Bang Sejeon^*

来源：Electronic Journal of Combinatorics, 2014, 21(1): P1.4.

• Distance-regular graph
• Girth
• Smallest eigenvalue
• Folded (2D+1)-cube

It is known that bipartite distance-regular graphs with diameter D %26gt;= 3, valency k %26gt;= 3, intersection number c(2) %26gt;= 2 and eigenvalues k = theta(0) %26gt; theta(1) %26gt; ... %26gt; theta(D) satisfy theta(1) %26lt;= k-2 and thus theta(D-1) %26gt;= 2-k. In this paper we classify non-complete distanceregular graphs with valency k 2, intersection numberc(2) %26gt;= 2 and an eigenvalue -k satisfying -k %26lt; theta %26lt;= 2-k. Moreover, we give a lower bound for valency k which implies OD 2 k for distance-regular graphs with girth g %26gt;= 5 satisfying g = 5 or g 3 (mod 4).

• 出版日期2014-1-12