# 2S3 transformation for Dyadic fractions in the interval (0, 1)

Document Type : Original paper

Authors

1 Department of Mathematics, Kariavattom Campus, University of Kerala, India

2 Department of Mathematics, University College, University of Kerala, Thiruvananthapuram, India

Abstract

The $2S3$ transformation, which was first described for positive integers, has been defined for dyadic rational numbers in the open interval $(0,1)$  in this study.  The set of dyadic rational numbers  is a Prüfer 2-group. For the dyadic $2S3$ transformation $T_{ds}(x)$, the restricted multiplicative and additive properties have been established. Graph parameters are used to generate more combinatorial outcomes for these properties. The relationship between the SM dyadic sum graph's automorphism group and the symmetric group has been investigated.

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