Throughout this chapter the symbol Γ = (V, f, E) will be used exclusively to denote a multigraph. Multigraphs have been studied far more than any other kind of system. They are the simplest interesting systems, since those with blocksize ≤ 1 have only trivial components. Another and perhaps more important reason for the extensive research in multigraphs is that they are the abstract mathematical objects which lie behind the many diagrams one often draws. Historically, multigraphs were first studied as topological objects.The vertices were points in the plane or 3-space, and the edges were simple arcs joining the vertices. As a result of these “graphic” beginnings, much of the terminology is geometric in spirit, and most of the results can be geometrically motivated. The reader is encouraged to draw pictures and to use them as an aid in following the proofs and doing the exercises.
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