5 papers
Algebraic connectivity in normed spaces
James Cruickshank, Sean Dewar, Derek Kitson
The algebraic connectivity of a graph in a finite dimensional real normed linear space is a geometric counterpart to the Fiedler number of the graph and can be regarded as…
The Rigid Unit Mode spectrum for symmetric frameworks
Eleftherios Kastis, Derek Kitson
We establish several fundamental properties of the Rigid Unit Mode (RUM) spectrum for symmetric frameworks with a discrete abelian symmetry group and arbitrary linear constraints.…
Automorphism Group of the Holomorph of a Cyclic Group
Kazuki Sato
We show that the holomorph of a cyclic group of order is isomorphic to its own automophism group when is twice of a power of an odd prime.
Edge-length preserving embeddings of graphs between normed spaces
Sean Dewar, Eleftherios Kastis, Derek Kitson +1
The concept of graph flattenability, initially formalized by Belk and Connelly and later expanded by Sitharam and Willoughby, extends the question of embedding finite metric spaces…
Block-and-hole graphs: Constructibility and -sparsity
Bryan Gin-ge Chen, James Cruickshank, Derek Kitson
We show that minimally 3-rigid block-and-hole graphs, with one block or one hole, are characterised as those which are constructible from by vertex splitting, and also, as th…