An elementary characterization of unretractive graphs
نویسنده
چکیده
The graphs studied in this paper are finite, undirected, without loops and multiple edges. A graph is called unretractive if it is isomorphic to each of its retracts. Unretractivity of graphs has been studied as a tool for generation and investigation of transformation groups. In particular the automorphism groups of graph products have been studied by Harary, Sabidussi, Hemminger, and Imrich and Klavzar. Knauer has studied various unretractive graphs and was mainly interested in algebraic properties of endomorphism monoids of graphs. The paper continues Knauer’s research. A condition is proposed that involves only elementary properties of graphs and characterizes unretractive graphs. The utility of that condition is shown by proving the unretractivity of a number of graphs or families of graphs.
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تاریخ انتشار 2007