Math 2.0

Combinatorics Definition

Maximum degree

Builds on Degree of a vertex

Definition

Let GG be a finite graph with a nonempty vertex set VV. The maximum degree of GG is Δ(G)=max⁡v∈Vdeg⁡(v),\Delta(G) = \max_{v \in V} \deg(v), the largest degree of a vertex of GG.

Remarks

The complete graph KnK_n has Δ=n−1\Delta = n - 1. A greedy colouring uses at most Δ(G)+1\Delta(G) + 1 colours. Brooks' theorem improves this to Δ(G)\Delta(G) in most cases.

Reading path

To understand this page from the ground up, read these 4 pages in order. The foundations come first.

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Graph, definition, no evidence levelGraphdefinitionNeighbourhood, definition, no evidence levelNeighbourhooddefinitionDegree of a vertex, definition, no evidence levelDegree of a vertexdefinitionMaximum degree, definition, no evidence levelMaximum degreedefinition
Each page uses the pages above it. The colour of the bar on a box shows how strong the evidence is, and the box also gives it as text. The list has the same pages.
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  1. Graph definition
  2. Neighbourhood definition
  3. Degree of a vertex definition
  4. Maximum degree definition

Where this leads

2 pages build on this one.

Further reading

  1. Web https://en.wikipedia.org/wiki/Degree_(graph_theory), Special values
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