Resources tagged with Networks/Graph Theory similar to Transitivity:
Other tags that relate to Transitivity
Number theory. Generalising. Mathematical reasoning & proof. Visualising. Inequality/inequalities. Combinatorics. Patterned numbers. Networks/Graph Theory. Manipulating algebraic expressions/formulae. Dynamical systems.There are 26 results
Knight Defeated
Stage: 4 Challenge Level: 
The knight's move on a chess board is 2 steps in one direction and one step in the other direction. Prove that a knight cannot visit every square on the board once and only (a tour) on a 2 by n board. . . .
Magic W Wrap Up
Stage: 5 Challenge Level:
Prove that you cannot form a Magic W with a total of 12 or less or with a with a total of 18 or more.
Tree Graphs
Stage: 4 Challenge Level:
A connected graph is a graph in which we can get from any vertex to any other by travelling along the edges. A tree is a connected graph with no closed circuits (or loops. Prove that every tree. . . .
Sprouts
Stage: 2, 3, 4 and 5
This article invites you to get familiar with a strategic game called "sprouts". The game is simple enough for younger children to understand, and has also provided experienced mathematicians. . . .
Some Circuits in Graph or Network Theory
Stage: 4 and 5
Eulerian and Hamiltonian circuits are defined with some simple examples and a couple of puzzles to illustrate Hamiltonian circuits.
Geometry and Gravity 2
Stage: 3, 4 and 5
This is the second of two articles and discusses problems relating to the curvature of space, shortest distances on surfaces, triangulations of surfaces and representation by graphs.
Cube Net
Stage: 5 Challenge Level:
How many tours visit each vertex of a cube once and only once? How many return to the starting point?
Symmetric Tangles
Stage: 4
The tangles created by the twists and turns of the Conway rope trick are surprisingly symmetrical. Here's why!
Euler's Formula and Topology
Stage: 4 and 5
Here is a proof of Euler's formula in the plane and on a sphere together with projects to explore cases of the formula for a polygon with holes, for the torus and other solids with holes and the. . . .
Sufficient but Not Necessary: Two Eyes and Seki in Go
Stage: 4
The game of go has a simple mechanism. This discussion of the principle of two eyes in go has shown that the game does not depend on equally clear-cut concepts.
Maximum Flow
Stage: 5 Challenge Level:
Given the graph of a supply network and the maximum capacity for flow in each section find the maximum flow across the network.
Behind the Rules of Go
Stage: 5
This article explains the use of the idea of connectedness in networks, in two different ways, to bring into focus the basics of the game of Go, namely capture and territory.
Ding Dong Bell
Stage: 3, 4 and 5
The reader is invited to investigate changes (or permutations) in the ringing of church bells, illustrated by braid diagrams showing the order in which the bells are rung.
Plum Tree
Stage: 4 and 5 Challenge Level:
Label a graph with the numbers 1 to n, one on each vertex, one on each arc. A Totally Magic graph is both Edge Magic and Vertex Magic.
W Mates
Stage: 5 Challenge Level:
Show there are exactly 12 magic labellings of the Magic W using the numbers 1 to 9. Prove that for every labelling with a magic total T there is a corresponding labelling with a magic total 30-T.
Olympic Magic
Stage: 4 Challenge Level:
in how many ways can you place the numbers 1, 2, 3 … 9 in the nine regions of the Olympic Emblem (5 overlapping circles) so that the amount in each ring is the same?
Magic Caterpillars
Stage: 4 and 5 Challenge Level:
Put numbers 1 to n on the edges and vertices of a graph so that the sum of the numbers on a vertex and on all arcs joined to that vertex is the same for all vertices.
Fermat's Poser
Stage: 4 Challenge Level:
Find the point whose sum of distances from the vertices (corners) of a given triangle is a minimum.
Instant Insanity
Stage: 5 Challenge Level:
Given the nets of 4 cubes with the faces coloured in 4 colours, build a tower so that on each vertical wall no colour is repeated, that is all 4 colours appear.
Magic W
Stage: 4 Challenge Level:
Find all the ways of placing the numbers 1 to 9 on a W shape, with 3 numbers on each leg, so that each set of 3 numbers has the same total.
The Four Colour Theorem
Stage: 3 and 4
The Four Colour Conjecture was first stated just over 150 years ago, and finally proved conclusively in 1976. It is an outstanding example of how old ideas can be combined with new discoveries. prove. . . .
Limiting Probabilities
Stage: 5 Challenge Level:
Given probabilities of taking paths in a graph from each node, use matrix multiplication to find the probability of going from one vertex to another in 2 stages, or 3, or 4 or even 100.
Euler's Formula
Stage: 5
Some simple ideas about graph theory with a discussion of a proof of Euler's formula relating the numbers of vertces, edges and faces of a graph.
The Use of Mathematics in Computer Games
Stage: 5
An account of how mathematics is used in computer games including geometry, vectors, transformations, 3D graphics, graph theory and simulations.
Classifying Solids Using Angle Deficiency
Stage: 3 and 4
Toni Beardon has chosen this article introducing a rich area for practical exploration and discovery in 3D geometry
Tangles
Stage: 3 and 4
A personal investigation of Conway's Rational Tangles. What were the interesting questions that needed to be asked, and where did they lead?
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