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Howida Al Fran

Doctor of Philosophy
Study Completed: 2017
College of Sciences


Thesis Title
The edge slide graph of the n-dimensional cube

Read article at Massey Research Online: MRO icon

A spanning tree of a connected network is a subnetwork that contains as few links as possible, while still keeping the network connected. They play an important role in the theory of networks. Ms Al Fran researched the structure of the spanning trees of the n-dimensional cube, by examining their edge slide graph: a network whose nodes are the spanning trees, with a link between two trees if they are related by a transformation called an edge slide. This is an operation that transforms one tree into another, by sliding an edge across a square face of the cube. Each spanning tree of the cube has an associated signature, which remains unchanged under edge slides. Ms Al Fran characterised and classified the possible signatures, and made substantial progress towards characterising the connected components of the edge slide graph in terms of signatures

Dr Christopher Tuffley
Dr David Simpson