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General Maths Unit 4 Topic 2
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Gravity
Graphs and networks
Key Concepts:
Terms in this set (41)
degree of the vertex
the number of edges that meet at a vertex
loop
an edge coming from a vertex back to the same vertex (attached twice)
multiple edges
edges that connect the same two vertices in a graph
isolated vertex
a vertex in a graph that is not connected to any other vertex by an edge
path
A walk (route) that has no repeated edges and no repeated vertices, can be open or closed
circuit
a trail (no repeated edges) that returns to its starting point (for a directed network, a circuit must have arcs in the same direction)
tree
a network, or part of a network that has no cycles or circuits
spanning tree
a tree that contains every node of a network
trail
a walk (any sequences of vertices) with no repeated edges, it may contain repeated vertices, can be open or closed
cycle
A closed path (no repeated vertices or edges) that starts and ends at the same vertex
connected graph
a graph that has no isolated vertices and no separate parts
bridge
an edge in a connected graph that, if removed, would cause the graph to no longer be connected
simple graph
a graph that does not have any loops and does not have any multiple edges
complete graphs
a graph that has an edge between every pair of vertices
directed graph/digraph
a graph where there is a direction associated with the edge (arc)
subgraph
a small section of an existing graph (with no extra vertices and no extra edges)
bipartite
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
weighted graph
a graph that has numbers, called weights, associated with the edges of a graph (weights often represent times, distances, etc)
walk
any connected sequence (route) of vertices, can be open or closed
edge or arc
the lines in a network
vertex
the points (dots) in a network
network
a type of graph that focusses on the connections (edges/arcs) between objects (vertices/nodes)
Adjacency Matrix
A matrix which records the number of direct links between vertices
Isomorphic (equivalent) graph
Graphs that contain identical information
Planar graph
A graph that can be drawn without any edges crossing
face
A region of a planar graph
Eulerian graph
graph that contains a closed trail (no repeated edges) that includes every edge of a graph
Semi-Eulerian graph
A graph that contains an open trail (no repeated edges) that involves every edge of the graph
Hamiltonian cycle
A closed path (no repeat edges, no repeat vertices) that visits every vertex of the graph. It starts and eds at the same vertex
Weighted graph
A graph with numbers (weights) associated with the edges of the graph. These weights represent physical quantities like time, distance, cost.
cost matrix
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.
activity network
A directed graph that represented the activities in a project
precedence table
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
Critical path
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.
Critical activity
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.
forward scanning
the process of determining the EST for each activity in a project. Take the largest value at each node.
backward scanning
the process of determining the LFT for each activity in a project. Take the smallest value at each vertex.
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