M
Mark E. Watkins
Researcher at University of Sydney
Publications - 84
Citations - 1678
Mark E. Watkins is an academic researcher from University of Sydney. The author has contributed to research in topics: Elliptic curve & Cayley graph. The author has an hindex of 22, co-authored 84 publications receiving 1569 citations. Previous affiliations of Mark E. Watkins include University of Melbourne & Pennsylvania State University.
Papers
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The groups of the generalized Petersen graphs
TL;DR: In this paper, the generalized Petersen graph G(n, k) was defined for integers n and k with 2 ≤ 2k < n, and G(5, 2) is the well known Petersen graph.
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Class numbers of imaginary quadratic fields
TL;DR: A modification of the Goldfeld-Oesterle work, which used an elliptic curve L-function with an order 3 zero at the central critical point to instead consider Dirichlet L-functions with low-height zeros near the real line, which agrees with the prediction of the Generalised Riemann Hypothesis.
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On the action of non-Abelian groups on graphs
TL;DR: In this paper, it was shown that the class of finite groups having the above regular representations is closed under the operation of direct product, and that for finite groups of order p 3 for p an odd prime (except for one group of order 27).
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Cayley maps
TL;DR: An algebraic theory of Cayley maps is presented and the theory is applied to determine exactly which regular or edge-transitive tilings of the sphere or plane are CayleyMaps or Cayley graphs.
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Graphical Regular Representations of Non-Abelian Groups, II
Lewis A. Nowitz,Mark E. Watkins +1 more
TL;DR: In this paper, it was shown that a given finite non-abelian group G has a graphical regular representation if (G|, 6) = 1 and an affirmative answer was given if G = 1.