廣義奇圖的值譜刻劃

Abstract

假設 G 是一個連接且k 正則圖型,其值譜和參數為 a_1=a_2=...=a_{d-1 }=0 但 a_d>0 的距離正則圖型.GAMMA.(也就是一個廣義奇圖)相同. 藉著 霍夫曼多項式(Hoffman Polynomial), 我們證明 G 必是距離正則圖型而 且和.GAMMA.有相同的相交陣列 (intersection array). 再者,如果. GAMMA.是下列圖型之一: the odd polygons, the odd graphs, the folded (2d+1)cube, the coset graph of binary Golay code, the Hoffman Singletion graph, the Gewirtz graph, the Higman Sims graph, the second constituent of the Higman Sims graph, 或 complement of the Clebsch graph, 則 G 和 .GAMMA. 同構. Suppose that G is connected, k-regular graph such that Spec(G)= Spec(.GAMMA.) where .GAMMA. is a distance regular graph with parameters a_1=a_2= ... =a_{d-1}=0 and a_d>0; i.e., a generalized odd graph, we show that G must be distance regular with the same intersection array as that of .GAMMA. in terms of the notion of Hoffman polynomials.