Split graphs whose half-strong endomorphisms form a monoid  

作　　者：LUO YanFeng ZHANG WenTing QIN YingYing HOU 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》2012年第6期1303-1320,共18页中国科学：数学（英文版）

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）, 1End（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 1End（X） = qEnd（X） for any split graph X. The conditions under which 1End（X） （resp. qEnd（X）） forms a submonoid of End（X） are also given. In particular, if hEnd（X） forms a monoid, then 1End（X） （resp. qEnd（X）） forms a monoid too.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：split graphs half-strong endomorphism locally strong endomorphism quasi-strong endomor-phism MONOID 

分 类 号：O157.5[理学—数学]