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The University of Edinburgh: Discrete Mathematics Graphs

For Students 10th - 12th
This article is an in-depth look at graphs. Topics covered are graph models, terminology, representations of graphs, graph isomorphism, connectivity, Euler and Hamiltonian Paths, and more. Examples and explanations are included.
Interactive
National Council of Teachers of Mathematics

Nctm: Illuminations: Graph Creator

For Students 3rd - 8th
Use this vertex-edge tool to create graphs and explore them. Investigate ideas such as planar graphs, complete graphs, minimum-cost spanning trees, and Euler and Hamiltonian paths.
Handout
Wolfram Research

Wolfram Math World: Hamiltonian Path

For Students 9th - 10th
A description of a Hamiltonian path, also called a Hamilton path.