Skip to content
Home
Path
Worksheets
Skill map
Leaderboard
Sign in
Save your progress
Search topics
Ctrl K
Sign in
Save your progress
Search
Skill map
General Mathematics
Graphs and networks
Chapter 10
0 of 32 strong
Weak only
Not started
RESTS ON
Classify row, column, square, symmetric and zero matrices
CH 8
Multiplication and division
CH 5
Graphs and networks
Adjacency matrices
Exploring and travelling
Weighted graphs and shortest paths
Dijkstra's algorithm
Trees and minimum connectors
Identify whether a graph is simple, contains an isolated vertex, is degenerate or is complete by checking its edge multiset
Decide whether every proposed vertex and edge belongs to a stated parent graph, without requiring the subgraph to retain every parent edge
Determine the number of edges in a complete simple graph, or the number still needed to complete a simple graph, by counting each unordered vertex pair once
Translate a factual description of objects and direct connections into the matching graph by assigning objects to vertices and relations to edges
Distinguish a route-between-two-vertices problem from an every-edge travel problem, an every-vertex travel problem and a minimum connector problem, then select the applicable graph method
Count the vertices, edges and loops of a displayed graph
Determine the degree of a named vertex and classify it as even or odd
Use sum of degrees = 2 × edges in both directions
Decide whether a graph is connected and identify separated groups
Identify the bridge or bridges of a connected graph
Decide whether two graphs are isomorphic by checking their structure
Distinguish planar form from the property of being planar
State the number of faces of a connected planar graph in planar form
Verify and solve v + f = e + 2 for a connected planar graph
Build the connection matrix of a network
Identify the network a connection matrix describes
Link connection-matrix symmetry to two-way connections
State the order of a matrix as rows × columns
Address an element by row and column subscripts, in both directions
Check whether a listed vertex sequence is a walk on a graph
Classify a valid walk as a trail, path, circuit or cycle
Decide whether a graph has an Eulerian trail, circuit, both or neither
Verify whether a listed route is an Eulerian trail or circuit
Verify whether a listed route is a Hamiltonian path or cycle
Read an edge weight and total the length of a stated route
Find the shortest path between two vertices by inspection
Apply Dijkstra's relaxation and permanent-labelling process from a stated source to determine exact shortest distances
Recover a shortest route from permanent distance labels and edge weights by tracing valid predecessors back to the source
Decide whether a graph or subgraph is a tree
Identify a spanning tree and compute its length
Determine a minimum spanning tree and its total weight
Recognise what a greedy algorithm is and where it applies