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A detailed tutorial on how to identify disconnected graphs. Step by step tutorial including several examples of disconnected graphs for reference.

A disconnected graph is a graph where not every single vertex is connected to all other vertices. Typically, graphs will have paths from all vertices, but if there is not a direct path from each and every vertex, then it is considered to be a disconnected graph. Some common shapes that are seen that are disconnected graphs are stars, rectangles, and hexagons. The opposite of a disconnected graph is a connected graph.

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A detailed tutorial on how to identify connected graphs. Step by step tutorial including several examples of connected graphs for reference.

A connected graph is a graph where every single vertex is connected to every other vertex. This does not mean to simply have a clear path from one vertex to another – it means there needs to be a direct path, or an edge, between two vertices. A triangle is a commonly seen shape that is a connected graph. The opposite of a connected graph is a disconnected graph.

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A detailed tutorial on polyhedrons. Step by step tutorial including several examples and a visual example of polyhedrons for reference.

Mathematicians have not yet decided what truely makes something a polyhedron, but in general they are accepted to be some 3D geometrical figure that has sides or faces, and usually at least one base. There are regular polyhedrons, which have all the same polygon making up their faces, and irregular polyhedrons – which are actually more common – where there are 2 or more shapes in them.

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A detailed tutorial on how to identify hexagons. Step by step tutorial including several examples of identifying hexagons for reference.

A hexagon is any polygon that has six sides. Hexagons can either be regular or irregular. Regular hexagons are close to the shape of a circle with 6 straight edges. Irregular hexagons are any other shape that has six sides, provided that it is still considered a polygon.