Graphs

This chapter describes the history of graphs and introduces the main definitions of graphs. It discusses some particular classes of graphs that we can meet in philosophy and provides some examples of them. The chapter presents a list of well-known graphs that we can put together according to their name. A graph generally has different kinds of drawings, but all of these are isomorphic. So, a graph is in fact a class of graphs generally defined up to an isomorphism. Even when graphs are non-separable, they always admit subgraphs. Informally speaking, the reconstruction conjecture says that graphs are determined uniquely by their subgraphs. The conjecture has been verified for a number of infinite classes of graphs: regular graphs, trees, disconnected graphs, unit interval graphs, separable graphs without end vertices, maximal planar graphs, maximal outerplanar graphs, outerplanar graphs and critical blocks.