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JOURNALS // Algebra and Discrete Mathematics // Archive
Algebra Discrete Math., 2018 Volume 26, Issue 2, Pages 270–279 (Mi adm683)
RESEARCH ARTICLE

A formula for the number of weak endomorphisms on paths

Ulrich Knauera, Nirutt Pipattanajindab

a Institut für Mathematik, Carl von Ossietzky Universität, D-26111 Oldenburg, Germany
b Faculty of Sciences and Technology, Kamphaeng Phet Rajabhat University, Kamphaeng Phet, Thailand

Abstract: A weak endomorphisms of a graph is a mapping on the vertex set of the graph which preserves or contracts edges. In this paper we provide a formula to determine the cardinalities of weak endomorphism monoids of finite undirected paths.

Keywords: path, weak endomorphisms, three-dimensional square lattices.

MSC: Primary 05C30; Secondary 05C38

Received: 24.11.2016
Revised: 09.12.2018

Language: English


© Steklov Math. Inst. of RAS, 2024