D1 Graphs and Networks Key Words (Chapter 2)

Walk

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

• A method of solving equations

• A type of graph traversal that visits all vertices

• A technique for optimizing network flow

Weight

• A measure of the heaviness of an object.

• A number that is associated with an Edge or Arc. It can represent distance, time, cost, etc.

• The total amount of matter in an object.

• A unit of measurement for temperature.

Trail

• is a Walk in which no Edge is visited more than once

• is a type of path that can be revisited

• is a route that includes multiple edges

• is a journey with no specific direction

Vertex Set

• 
• A collection of all the edges in a graph

• A set of vertices that are not connected

• A group of faces in a polyhedron

Weighted Graphs

• A graph that has a number associated with each edge or arc. This is an alternative name for a Network.

• A graph that represents data in a linear format.

• A graph that only contains vertices without edges.

• A graph that is used to display hierarchical data.

Bipartite Graph

• A graph where all vertices are connected to every other vertex.

• A graph whose vertices can be divided into two disjoint sets such that no two graph vertices within the same set are adjacent.

• A graph that contains cycles of odd length.

• A graph that has at least one vertex with a degree of zero.

Complete Graph

• A graph in which there is an edge between every pair of vertices.

• A graph that contains no edges.

• A graph that is disconnected.

• A graph with only one vertex.

Graph

• A collection of random points in space

• A set of Vertices or Nodes which are connected together by Edges or Arcs

• A linear arrangement of numbers

• A diagram representing a function

Adjacent Vertices

• Two vertices that are connected by a single edge.

• Two vertices that are not connected by any edge.

• Two vertices that are connected by multiple edges.

• Two vertices that are at the same position.

Path

• A sequence of edges connecting vertices.

• A walk in which no vertex is visited more than once.

• A closed loop in a graph.

• A collection of all vertices in a graph.