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General Maths Unit 4 Topic 2
Graphs and networks
Terms in this set (41)
degree of the vertex
the number of edges that meet at a vertex
an edge coming from a vertex back to the same vertex (attached twice)
edges that connect the same two vertices in a graph
a vertex in a graph that is not connected to any other vertex by an edge
A walk (route) that has no repeated edges and no repeated vertices, can be open or closed
a trail (no repeated edges) that returns to its starting point (for a directed network, a circuit must have arcs in the same direction)
a network, or part of a network that has no cycles or circuits
a tree that contains every node of a network
a walk (any sequences of vertices) with no repeated edges, it may contain repeated vertices, can be open or closed
A closed path (no repeated vertices or edges) that starts and ends at the same vertex
a graph that has no isolated vertices and no separate parts
an edge in a connected graph that, if removed, would cause the graph to no longer be connected
a graph that does not have any loops and does not have any multiple edges
a graph that has an edge between every pair of vertices
a graph where there is a direction associated with the edge (arc)
a small section of an existing graph (with no extra vertices and no extra edges)
a graph with vertices that can be divided into two distinct sets and every edge joins at a vertex in one set to a vertex in another set
a graph that has numbers, called weights, associated with the edges of a graph (weights often represent times, distances, etc)
any connected sequence (route) of vertices, can be open or closed
edge or arc
the lines in a network
the points (dots) in a network
a type of graph that focusses on the connections (edges/arcs) between objects (vertices/nodes)
A matrix which records the number of direct links between vertices
Isomorphic (equivalent) graph
Graphs that contain identical information
A graph that can be drawn without any edges crossing
A region of a planar graph
graph that contains a closed trail (no repeated edges) that includes every edge of a graph
A graph that contains an open trail (no repeated edges) that involves every edge of the graph
A closed path (no repeat edges, no repeat vertices) that visits every vertex of the graph. It starts and eds at the same vertex
A graph with numbers (weights) associated with the edges of the graph. These weights represent physical quantities like time, distance, cost.
A table of weights for a complete bipartite graph. It contains the cost in terms of time, money or other quantities, of assigning objects from one group to objects in another.
A directed graph that represented the activities in a project
Identifies all activities in a project and their immediate predecessor
float (slack) time
The largest amount of time by which an activity can be delayed without affecting the overall completion time of the project
The sequence of activities that cannot be delayed without affecting the overall completion of the project.
Earliest start time
The earliest time an activity can begin after all predecessors have been completed.
Latest start time
The latest time an activity can begin after all predecessors have been completed.
Activities that have the same EST and LST
Latest finishing time
The latest time an activity can finish without affecting the overall completion time of the project.
the process of determining the EST for each activity in a project. Take the largest value at each node.
the process of determining the LFT for each activity in a project. Take the smallest value at each vertex.
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