Merging in Antipodal Distance-Regular Graphs
نویسندگان
چکیده
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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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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Antipodal covers of strongly regular graphs which are not necessarily distance-regular are studied. The structure of short cycles in an antipodal cover is considered. In most cases, this provides a tool to determine if a strongly regular graph has an antipodal cover. In these cases, covers cannot be distance-regular except when they cover a complete bipartite graph. A relationship between antip...
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ژورنال
عنوان ژورنال: Journal of Combinatorial Theory, Series B
سال: 1994
ISSN: 0095-8956
DOI: 10.1006/jctb.1994.1066