Abstract
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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1977 Springer-Verlag, New York Inc.
About this chapter
Cite this chapter
Graver, J.E., Watkins, M.E. (1977). Multigraphs. In: Combinatorics with Emphasis on the Theory of Graphs. Graduate Texts in Mathematics, vol 54. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-9914-1_3
Download citation
DOI: https://doi.org/10.1007/978-1-4612-9914-1_3
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-9916-5
Online ISBN: 978-1-4612-9914-1
eBook Packages: Springer Book Archive