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D-saturated property of the Cayley graphs of semigroups

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Abstract

Let D be a finite graph. A semigroup S is said to be Cayley D-saturated with respect to a subset T of S if, for all infinite subsets V of S, there exists a subgraph of Cay(S,T) isomorphic to D with all vertices in V. The purpose of this paper is to characterize the Cayley D-saturated property of a semigroup S with respect to any subset T⊆S. In particular, the Cayley D-saturated property of a semigroup S with respect to any subsemigroup T is characterized.

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Authors and Affiliations

  1. Department of Mathematics, Lanzhou University, Lanzhou, 730000, People’s Republic of China

    Dong Yang & Xing Gao

Authors
  1. Dong Yang
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  2. Xing Gao
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Correspondence to Xing Gao.

Additional information

Communicated by Thomas E. Hall.

This research was partially supported by the National Natural Science Foundation of China (No.10571077) and the Natural Science Foundation of Gansu Province (No.3ZS052-A25-017).

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Yang, D., Gao, X. D-saturated property of the Cayley graphs of semigroups. Semigroup Forum 80, 174–180 (2010). https://doi.org/10.1007/s00233-009-9195-4

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  • DOI: https://doi.org/10.1007/s00233-009-9195-4

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