10 citations · 31 across the 11 of their papers we have counts for
12 papers
Lobe, Edge, and Arc Transitivity of Graphs of Connectivity 1
Jack E. Graver, Mark E. Watkins
We give necessary and sufficient conditions for lobe-transitivity of locally finite and locally countable graphs whose connectivity equals 1. We show further that, given any biconn…
Growth of Face-Homogeneous Tessellations
Stephen J. Graves, Mark E. Watkins
A tessellation of the plane is face-homogeneous if for some integer there exists a cyclic sequence of integers such that, for every fa…
Infinite Motion and 2-Distinguishability of Graphs and Groups
Wilfried Imrich, Simon M. Smith, Thomas W. Tucker +1
A group A acting faithfully on a set X is 2-distinguishable if there is a 2-coloring of X that is not preserved by any nonidentity element of A, equivalently, if there is a proper…
Bounding the distinguishing number of infinite graphs
Simon M. Smith, Mark E. Watkins
A group of permutations G of a set V is k-distinguishable if there exists a partition of V into k parts such that only the identity permutation in G fixes setwise all of the cells…
Distinguishability of infinite groups and graphs
Simon M. Smith, Thomas W. Tucker, Mark E. Watkins
The {\em distinguishing number} of a group acting faithfully on a set is the least number of colors needed to color the elements of so that no non-identity element of t…
Some heuristics about elliptic curves
Mark Watkins
We give some heuristics for counting elliptic curves with certain properties. In particular, we re-derive the Brumer-McGuinness heuristic for the number of curves with positive/neg…