Graphs vocab

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9 Terms

1
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Kn
Complete graph on n vertices, every pair of vertices is connected.
2
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Cn
Cycle graph on n vertices.
3
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Wn
Wheel graph with a cycle of n vertices plus one center vertex.
4
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Kn,m
Complete bipartite graph with partitions of sizes n and m.
5
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Cut edge
An edge whose removal increases the number of connected components.
6
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Acyclic
Containing no cycles.
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Handshaking theorem
The sum of all vertex degrees equals twice the number of edges.
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Euler circuit test
A graph has an Euler circuit if and only if every vertex has even degree and the graph is connected ignoring isolated vertices.
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Maximum degree bound
If D is the maximum degree, G can be colored with D plus 1 colors.