Naturally ordered strong endomorphisms on graphs

Abstract

© 2019, Springer Japan KK, part of Springer Nature. In this paper, we study the natural partial order ≤ on SEnd(G), the strong endomorphism monoid of a finite graph G and characterize minimal elements and maximal elements of (SEnd(G) , ≤). Then we introduce the concept of connectedness on (SEnd(G) , ≤) by using the natural partial order ≤ and determine the number of connected components of SEnd(G) under certain conditions.