From nut graphs to molecular structure and conductivity

Abstract

This book relates our experience of an enjoyable, often bumpy, passage that started with Irene's attempt to answer a simple mathematical curiosity, way back in 1994. Prompted by Stanley Fiorini, she embarked on the task of identifying graphs whose adjacency matrix has small rank. By the time she reached rank five, it was clear that computer searches were necessary. From then on, a door opened wide into a garden that kept on increasing in size showing budding flowery plants of exciting mathematical novelties, often not easily accessible, waiting to be developed and nurtured. Our mood tended to mimic the peaks and troughs of the tour following the growth and wilting of our mathematical foliage. [Excerpt from the Preface]