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The Action of \(SL(2,{\mathbb {C}})\) on Hyperbolic 3-Space and Orbital Graphs

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Abstract

In this paper we discuss the action of \(SL(2,{\mathbb {C}})\) on hyperbolic 3-space using quaternions. And then we investigate suborbital graphs for the special subgroup of \(PSL(2,\mathbb {C})\). We point out the relation between elliptic elements and circuits in graphs. Results obtained by the method used are important because they mean that suborbital graphs have a potential to explain signature problems.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Arts and Sciences, Pamukkale University, Denizli, Turkey

    Murat Beşenk

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  1. Murat Beşenk
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Correspondence to Murat Beşenk.

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Beşenk, M. The Action of \(SL(2,{\mathbb {C}})\) on Hyperbolic 3-Space and Orbital Graphs. Graphs and Combinatorics 34, 545–554 (2018). https://doi.org/10.1007/s00373-018-1893-9

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  • DOI: https://doi.org/10.1007/s00373-018-1893-9

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