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End-regular and End-orthodox generalized lexicographic products of bipartite graphs

Rui Gu; Hailong Hou — 2016

Open Mathematics

A graph X is said to be End-regular (End-orthodox) if its endomorphism monoid End(X) is a regular (orthodox) semigroup. In this paper, we determine the End-regular and the End-orthodox generalized lexicographic products of bipartite graphs.

The join of split graphs whose completely regular endomorphisms form a monoid

Hailong Hou; Yanhua Song; Rui Gu — 2017

Open Mathematics

In this paper, completely regular endomorphisms of the join of split graphs are investigated. We give conditions under which all completely regular endomorphisms of the join of two split graphs form a monoid.

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