منابع مشابه
From regular boundary graphs to antipodal distance-regular graphs
Let Γ be a regular graph with n vertices, diameter D, and d + 1 different eigenvalues λ > λ1 > · · · > λd. In a previous paper, the authors showed that if P (λ) > n − 1, then D ≤ d − 1, where P is the polynomial of degree d−1 which takes alternating values±1 atλ1, . . . , λd. The graphs satisfying P (λ) = n − 1, called boundary graphs, have shown to deserve some attention because of their rich ...
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Throughout this paper, we assume 1 is a connected finite undirected graph without loops or multiple edges. We identify 1 with the set of vertices. For vertices : and ; in 1, let (:, ;) denote the distance between : and ; in 1, that is, the length of a shortest path connecting : and ;. Let d=d(1 ) denote the diameter of 1, that is, the maximal distance between any two vertices in 1. Let 1i (:)=[...
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Let G be a non-bipartite strongly regular graph on n vertices of valency k. We prove that if G has a distance-regular antipodal cover of diameter 4, then k ≤ 2(n + 1)/5 , unless G is the complement of triangular graph T (7), the folded Johnson graph J (8, 4) or the folded halved 8-cube. However, for these three graphs the bound k ≤ (n − 1)/2 holds. This result implies that only one of a complem...
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Let Γ be a regular (connected) graph with n vertices and d + 1 distinct eigenvalues. As a main result, it is shown that Γ is an r-antipodal distanceregular graph if and only if the distance graph Γd is constituted by disjoint copies of the complete graph Kr, with r satisfying an expression in terms of n and the distinct eigenvalues. AMS subject classifications. 05C50 05E30
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ژورنال
عنوان ژورنال: Bulletin of the Australian Mathematical Society
سال: 1989
ISSN: 0004-9727,1755-1633
DOI: 10.1017/s0004972700002793