University of Hertfordshire Research Archive

        JavaScript is disabled for your browser. Some features of this site may not work without it.

        Browse

        All of UHRABy Issue DateAuthorsTitlesThis CollectionBy Issue DateAuthorsTitles

        Arkivum Files

        My Downloads
        View Item 
        • UHRA Home
        • University of Hertfordshire
        • Research publications
        • View Item
        • UHRA Home
        • University of Hertfordshire
        • Research publications
        • View Item

        The Maximal Subgroups and the Complexity of the Flow Semigroup of Finite (Di)graphs

        View/Open
        Pre_Print_Version.pdf (PDF, 779Kb)
        1705.09577v2.pdf (PDF, 685Kb)
        Author
        Horváth, Gábor
        Nehaniv, Chrystopher
        Podoski, Károly
        Attention
        2299/19641
        Abstract
        The flow semigroup, introduced by John Rhodes, is an invariant for digraphs and a complete invariant for graphs. We refine and prove Rhodes's conjecture on the structure of the maximal groups in the flow semigroup for finite, antisymmetric, strongly connected graphs. Building on this result, we investigate and fully describe the structure and actions of the maximal subgroups of the flow semigroup acting on all but k points for all finite digraphs and graphs for all k >=1. A linear algorithm is presented to determine these so-called 'defect k groups' for any finite (di)graph. Finally, we prove that the complexity of the flow semigroup of a 2-vertex connected (and strongly connected di)graph with n vertices is n- 2, completely confirming Rhodes's conjecture for such (di)graphs.
        Publication date
        2017-11-30
        Published in
        International Journal of Algebra and Computation
        Published version
        https://doi.org/10.1142/S0218196717500412
        Other links
        http://hdl.handle.net/2299/19641
        Metadata
        Show full item record
        Keep in touch

        © 2019 University of Hertfordshire

        I want to...

        • Apply for a course
        • Download a Prospectus
        • Find a job at the University
        • Make a complaint
        • Contact the Press Office

        Go to...

        • Accommodation booking
        • Your student record
        • Bayfordbury
        • KASPAR
        • UH Arts

        The small print

        • Terms of use
        • Privacy and cookies
        • Criminal Finances Act 2017
        • Modern Slavery Act 2015
        • Sitemap

        Find/Contact us

        • T: +44 (0)1707 284000
        • E: ask@herts.ac.uk
        • Where to find us
        • Parking
        • hr
        • qaa
        • stonewall
        • AMBA
        • ECU Race Charter
        • disability confident
        • AthenaSwan