Split graphs whose half-strong endomorphisms form a monoid

查看全文 作　　者：LUO [1]YanFeng;ZHANG [1]WenTing;QIN [2]YingYing;HOU [3]HaiLonga

机构地区：[1]Department of Mathematics, Lanzhou University, Lanzhou 730000, China;[2]Department of Mathematics and Physics, Wuyi University, Jiangmen 529020, China;[3]School of Mathematics and Statistics, Henan University of Science and Technology, Luoyang 471003, China

出　　处：《Science China Mathematics》索引2012年第55卷第6期,共18页

基　　金：supported by National Natural Science Foundation of China(Grant Nos. 10571077,10971086) 摘　　要：In this paper,the half-strong,the locally strong and the quasi-strong endomorphisms of a split graph are investigated.Let X be a split graph and let End(X),hEnd(X),lEnd(X) and qEnd(X) be the endomorphism monoid,the set of all half-strong endomorphisms,the set of all locally strong endomorphisms and the set of all quasi-strong endomorphisms of X,respectively.The conditions under which hEnd(X) forms a submonoid of End(X) are given.It is shown that lEnd(X) = qEnd(X) for any split graph X.The conditions under which lEnd(X)(resp.qEnd(X)) forms a submonoid of End(X) are also given.In particular,if hEnd(X) forms a monoid,then lEnd(X)(resp.qEnd(X)) forms a monoid too. 关键词：强自同态分裂图自同态幺半群集合

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Split graphs whose half-strong endomorphisms form a monoid

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