کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
8903857 | 1632963 | 2018 | 30 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Partially metric association schemes with a multiplicity three
ترجمه فارسی عنوان
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کلمات کلیدی
طرح انجمن، نمودار 2-راه رفتن منظم، چندگانگی کوچک، گراف منظم منظم، پوشش مکعب،
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات گسسته و ترکیبات
چکیده انگلیسی
An association scheme is called partially metric if it has a connected relation whose distance-two relation is also a relation of the scheme. In this paper we determine the symmetric partially metric association schemes with a multiplicity three. Besides the association schemes related to regular complete 4-partite graphs, we obtain the association schemes related to the Platonic solids, the bipartite double scheme of the dodecahedron, and three association schemes that are related to well-known 2-arc-transitive covers of the cube: the Möbius-Kantor graph, the Nauru graph, and the Foster graph F048A. In order to obtain this result, we also determine the symmetric association schemes with a multiplicity three and a connected relation with valency three. Moreover, we construct an infinite family of cubic arc-transitive 2-walk-regular graphs with an eigenvalue with multiplicity three that give rise to non-commutative association schemes with a symmetric relation of valency three and an eigenvalue with multiplicity three.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Combinatorial Theory, Series B - Volume 130, May 2018, Pages 19-48
Journal: Journal of Combinatorial Theory, Series B - Volume 130, May 2018, Pages 19-48
نویسندگان
Edwin R. van Dam, Jack H. Koolen, Jongyook Park,