Using twins and scaling to construct cospectral graphs for the normalized Laplacian

The spectrum of the normalized Laplacian matrix cannot determine the number of edges in a graph, however finding constructions of cospectral graphs with differing number of edges has been elusive. In this paper we use basic properties of twins and scaling to show how to construct such graphs. We also give examples of families of graphs which are cospectral with a subgraph for the normalized Laplacian matrix

Study Bugs do a poster presentation

The poster describes the concepts behind, and the development of, a series of short films which deliver study skills information to students using an informal, imaginative and slightly quirky style. The stars of the films are the study bugs, who have taken on a life of their own, presenting important information in their own inimitable style. The videos have been used in teaching sessions, at Derby and other universities, to reinforce taught content and engage students in discussion. The films are available online through YouTube and can be embedded into VLEs. They have had positive feedback from academics and students. The films are accessible to students from different academic and cultural backgrounds, highlighting core concepts in a straightforward manner