Colloquium on Tuesday, March 5, 2019 at 15:30 in Room 306 Alan Turing:

 

Speaker:   Gerhard Kling (SOAS University of London and The Open University)

 

Title:     On the uniqueness of the Laplacian spectra of coalescence of complete graphs

 

Abstract:

Using coalescence and cones, this study defines three types of graphs formed by amalgamating vertices of disjoint unions of complete graphs. The three types include the cone over a disjoint union of two complete graphs (C1), the cone over a disjoint union of k complete graphs (C2), and the l cone over a disjoint union of two complete graphs (C3). Coalescence of complete graphs (C1, C3) and the l cone (C3) are determined by their Laplacian spectra, a novel finding. Their Laplacian spectra reveal the size of the vertex cutset. Applications include the analysis of corporate networks, where individuals form coalescence of complete graphs through joint membership of two or more company boards.