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Shannon multigraph information


In the mathematical discipline of graph theory, Shannon multigraphs, named after Claude Shannon by Vizing (1965), are a special type of triangle graphs, which are used in the field of edge coloring in particular.

A Shannon multigraph is multigraph with 3 vertices for which either of the following conditions holds:
  • a) all 3 vertices are connected by the same number of edges.
  • b) as in a) and one additional edge is added.

More precisely one speaks of Shannon multigraph Sh(n), if the three vertices are connected by , and edges respectively. This multigraph has maximum degree n. Its multiplicity (the maximum number of edges in a set of edges that all have the same endpoints) is .

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