Automorphism groups of graph covers and uniform subset graphs

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2018

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Taylor and Francis Group

Abstract

Hofmeister considered the automorphism groups of antipodal graphs through the exploration of graph covers. In this note weextend the exploration of automorphism groups of distance preserving graph covers. We apply the technique of graph covers todetermine the automorphism groups of uniform subset graphsΓ(2k,k,k−1) andΓ(2k,k,1).The determination of automorphismgroups answers a conjecture posed by Mark Ramras and Elizabeth Donovan. They conjectured that Aut(Γ(2k,k,k−1))∼=S2k×<T>,whereTis the complementation mapX↦→T(X)=Xc={1,2,...,2k}\X,andXis ak-subset ofΩ={1,2,...,2k}.

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Mathematics, Engineering, Applied Mathematics, Physics

Citation

Mumba, N., & Mwambene, E. (2018). Automorphism groups of graph covers and uniform subset graphs. AKCE International Journal of Graphs and Combinatorics, 15(1), 27-30. https://doi.org/10.1016/j.akcej.2018.01.016

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https://doi.org/10.1016/j.akcej.2018.01.016
 http://hdl.handle.net/10566/8353

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Research Articles (Mathematics)