Graphs and Combinatorics

, Volume 35, Issue 6, pp 1619–1632 | Cite as

Naturally ordered strong endomorphisms on graphs

  • Nirutt Pipattanajinda
  • Yangkok KimEmail author
  • Srichan Arworn
Original Paper


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


Natural partial orders Strong endomorphism monoid Graph 

Mathematics Subject Classification

20M10 06A06 05C25 



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Copyright information

© Springer Japan KK, part of Springer Nature 2019

Authors and Affiliations

  • Nirutt Pipattanajinda
    • 1
  • Yangkok Kim
    • 2
    Email author
  • Srichan Arworn
    • 3
  1. 1.Program of Mathematics, Faculty of Sciences and TechnologyKamphaeng Phet Rajabhat UniversityKamphaeng PhetThailand
  2. 2.Department of MathematicsDongeui UniversityBusanRepublic of Korea
  3. 3.Department of Mathematics, Faculty of SciencesChiang Mai UniversityChiang MaiThailand

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