James Cruickshank

collaborators

4 papers

math.CO2025

Algebraic connectivity in normed spaces

James Cruickshank, Sean Dewar, Derek Kitson

The algebraic connectivity of a graph $G$ in a finite dimensional real normed linear space $X$ is a geometric counterpart to the Fiedler number of the graph and can be regarded as…

math.HO2025

Rigidity of Graphs and Frameworks: A Matroid Theoretic Approach

James Cruickshank, Bill Jackson, Tibor Jordán +1

A $d$ -dimensional (bar-and-joint) framework $(G, p)$ consists of a graph $G = (V, E)$ and a realisation $p : V \to R^{d}$ . It is rigid if every continuous motion of the vertices wh…

math.CO2025

Volume Rigidity of Simplicial Manifolds

James Cruickshank, Bill Jackson, Shin-ichi Tanigawa

Classical results of Cauchy and Dehn imply that the 1-skeleton of a convex simplicial polyhedron $P$ is rigid i.e. every continuous motion of the vertices of $P$ in $R^{3}$ w…

math.GR2024

Automorphism Group of the Holomorph of a Cyclic Group

Kazuki Sato

We show that the holomorph of a cyclic group of order $n$ is isomorphic to its own automophism group when $n$ is twice of a power of an odd prime.