On Combinatorial Properties of Bands

Abstract

In this paper we study the D-saturated property of bands defined in terms of their Cayley graphs Cay(S,C), where S is a band and C ⊆ Z(S), the center of S. Also we characterize the Cayley graphs of bands. More generally, for a finite graph Γ =Cay(T, D), where T is a band and D ⊆ Z(T), we give an algorithm for finding all bands S and C ⊆ Z(S) such that Γ =Cay(S, C).

Key Words:

• Bands
• Cayley graphs of semigroups
• Cayley graphs of bands and semilattices
• D-saturated property

2010 Mathematics Subject Classification:

• Primary: 05C25
• Secondary: 05C20

ACKNOWLEDGMENT

The authors are grateful to the referee for valuable suggestions and corrections, which helped us to improve and correct the manuscript.

Notes

Communicated by V. Gould.