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1. THE DIGRAPH OF THE SYMMETRIC INVERSE TRANSFORMATION SEMIGROUP by Ugbene Ifeanyichukwu Jeff and Emunefe John Obatarhe Volume 59 (January – March 2021 Issue)
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THE DIGRAPH OF THE SYMMETRIC INVERSE TRANSFORMATION SEMIGROUP

*1Ugbene Ifeanyichukwu Jeff and 2Emunefe John Obatarhe

1Department of Mathematics, Federal University of Petroleum Resources, Effurun,

Delta State, Nigeria.

2Department of General Studies, Mathematics and Statistics Unit, Petroleum

Training Institute, Effurun, Delta State, Nigeria.

 

Abstract

Enumeration of a combinatorial nature in the study transformation semigroup is inevitable and a digraph of transformation is naturally formed given any transformation semigroup.

Let X_n={1,2,…,n}  be a finite set on which the domain and range of the partial injective (symmetric inverse) transformations is defined. We characterized its strongly, unilateral and weakly connected digraphs and found its cardinality. Also cardinality of its hamiltonian, eulerian and acyclic digraphs were characterized.

Keywords: Digraph of transformation, Symmetric Inverse transformation semigroup, Connected, Hamiltonian, Eulerian, Acyclic Digraphs.  

MSC: 

20M20 Semigroups of transformations, relations, partitions etc.

05C30 Enumeration in graph theory

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