Graph Theory

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14 Terms

1

Nodes

Vertices or Vertex Set

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2

Degree/ Order/ Valency

Number of edges coming off a vertice

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3

Walk

A route through a graph along edges from one vertex to the next

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4

Path

A walk where no vertex is visited more than once

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5

Trail

A walk where no edge is visited more than once

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6

Cycle

A walk which the end vertex is the same as the start vertex where no other vertex is visited more than once

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7

Hamiltonian Cycle

A cycle that includes every vertex

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8

Tree

A connected graph with no cycles

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9

Spanning Tree

Includes all vertices and is a tree

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10

Complete Graph

Every vertex is directly connected by a single edge to each of the other vertices

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11

Isomorphic Graph

Show the same information but may be drawn differently

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12

Planar Graph

One that can be drawn in a plane such that no 2 edges meet except at a vertex

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13

Eulerian Graph

Covers every edge exactly once can start and end at any vertex. The degree of each vertice is even

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14

Semi-Eulerian Graphs

Same as Eulerian but ends on a different vertex. It always has two odd degrees

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