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	A family of symmetric graphs with complete quotients
	Fang, Teng ; Fang, Xin Gui ; Xia, Binzhou ; Zhou, Sanming
	2016
关键词	Symmetric graph arc-transitive graph almost multicover AUTOMORPHISM-GROUPS PERMUTATION-GROUPS TRANSITIVE GRAPHS DESIGNS
英文摘要	A finite graph Gamma is G-symmetric if it admits G as a group of automorphisms acting transitively on V(Gamma) and transitively on the set of ordered pairs of adjacent vertices of Gamma. If V(Gamma) admits a nontrivial G-invariant partition B such that for blocks B, C is an element of B adjacent in the quotient graph Gamma(B) relative to B, exactly one vertex of B has no neighbour in C, then we say that Gamma is an almost multicover of Gamma(B). In this case there arises a natural incidence structure D(Gamma, B) with point set B. If in addition Gamma(B) is a complete graph, then D(Gamma, B) is a (G, 2)-point-transitive and G-block -transitive 2-(vertical bar B vertical bar, m + 1, lambda) design for some m >= 1, and moreover either lambda = 1 or lambda = m + 1. In this paper we classify such graphs in the case when lambda = m + 1; this together with earlier classifications when lambda = 1 gives a complete classification of almost multicovers of complete graphs.; China Scholarship Council (CSC); National Science Foundation of China [NSFC 11501011]; Australian Research Council [FT110100629]; MRGSS grant of the University of Melbourne; SCI(E); ARTICLE; 2; 23
语种	英语
出处	SCI
出版者	ELECTRONIC JOURNAL OF COMBINATORICS
内容类型	其他
源URL	[http://hdl.handle.net/20.500.11897/458993]
专题	数学科学学院
推荐引用方式 GB/T 7714	Fang, Teng,Fang, Xin Gui,Xia, Binzhou,et al. A family of symmetric graphs with complete quotients. 2016-01-01.

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