Affine flag graphs and classification of a family of symmetric graphs with complete quotients
نویسندگان
چکیده
منابع مشابه
Unitary graphs and classification of a family of symmetric graphs with complete quotients
A finite graph Γ is called G-symmetric if G is a group of automorphisms of Γ which is transitive on the set of ordered pairs of adjacent vertices of Γ. We study a family of symmetric graphs, called the unitary graphs, whose vertices are flags of the Hermitian unital and whose adjacency relations are determined by certain elements of the underlying finite fields. Such graphs admit the unitary gr...
متن کاملA Family of Symmetric Graphs with Complete Quotients
A finite graph Γ is G-symmetric if it admits G as a group of automorphisms acting transitively on V (Γ) and transitively on the set of ordered pairs of adjacent vertices of Γ. If V (Γ) admits a nontrivial G-invariant partition B such that for blocks B,C ∈ B adjacent in the quotient graph ΓB relative to B, exactly one vertex of B has no neighbour in C, then we say that Γ is an almost multicover ...
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In this paper we give a classification of a family of symmetric graphs with complete 2-arc transitive quotients. Of particular interest are two subfamilies of graphs which admit an arc-transitive action of a projective linear group. The graphs in these subfamilies can be defined in terms of the cross ratio of certain 4-tuples of elements of a finite projective line, and thus may be called the s...
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With any G-symmetric graph admitting a nontrivial G-invariant partition B, we may associate a natural ‘‘cross-sectional’’ geometry, namely the 1-design DðBÞ 1⁄4 ðB; BðBÞ; IÞ in which IC for 2B and C 2 BðBÞ if and only if is adjacent to at least one vertex in C, where B2B and BðBÞ is the neighbourhood of B in the quotient graph B of with respect to B. In a vast number of cases, the dual 1-design...
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فرض کنیمg یک گروه غیر آبلی متناهی باشد . گراف جابجایی g که با نماد نمایش داده می شود ،گرافی است ساده با مجموعه رئوس که در آن دو راس با یک یال به هم وصل می شوند اگر و تنها اگر . مکمل گراف جابجایی g راگراف نا جابجایی g می نامیم.و با نماد نشان می دهیم. گرافهای جابجایی و ناجابجایی یک گروه متناهی ،اولین بار توسطاردوش1 مطرح گردید ،ولی در سالهای اخیر به طور مفصل در مورد بحث و بررسی قرار گرفتند . در ،م...
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ژورنال
عنوان ژورنال: Discrete Mathematics
سال: 2019
ISSN: 0012-365X
DOI: 10.1016/j.disc.2019.02.017