In the paper we introduce and study a classification of finite (simple, undirected, loopless) graphs with respect to a switch-equivalence (`local-complement' equivalence of \cite{pascvebl}, an analogue of the complement-equivalence of \cite{conell}). In the paper we propose a simple inductive method to compute the number of switch-types of graphs on $n$ vertices and we show that there are exactly 16 such types of graphs on 6 vertices.
Introduction * Definitions and examples* Paths and cycles* Trees* Planarity* Colouring graphs* Matching, marriage and Menger's theorem* Matroids Appendix 1: Algorithms Appendix 2: Table of numbers List of symbols Bibliography Solutions to selected exercises Index
Berzelius failed to make use of Faraday's electrochemical laws in his laborious determination of equivalent weights.