In this paper, we describe the canonical partial order on the idempotent set of the strong endomorphism monoid of a graph, and using this we further characterize primitive idem potenes from the viewpoint of combinator...In this paper, we describe the canonical partial order on the idempotent set of the strong endomorphism monoid of a graph, and using this we further characterize primitive idem potenes from the viewpoint of combinatorics. The number of them is also given.展开更多
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 ...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.展开更多
文摘In this paper, we describe the canonical partial order on the idempotent set of the strong endomorphism monoid of a graph, and using this we further characterize primitive idem potenes from the viewpoint of combinatorics. The number of them is also given.
基金supported by National Natural Science Foundation of China(Grant Nos. 10571077,10971086)
文摘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.
