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2. Chvátal graph - Wikipedia

   en.wikipedia.org/wiki/Chvátal_graph

   Its chromatic number is 4: it can be colored using four colors, but not using only three. It is, as Chvátal observes, the smallest possible 4-chromatic 4-regular triangle-free graph; the only smaller 4-chromatic triangle-free graph is the Grötzsch graph, which has 11 vertices but has maximum degree 5 and is not regular. [1]

3. Barycentric coordinate system - Wikipedia

   en.wikipedia.org/wiki/Barycentric_coordinate_system

   A 3-simplex, with barycentric subdivisions of 1-faces (edges) 2-faces (triangles) and 3-faces (body). In geometry, a barycentric coordinate system is a coordinate system in which the location of a point is specified by reference to a simplex (a triangle for points in a plane, a tetrahedron for points in three-dimensional space, etc.).

4. 1 + 2 + 3 + 4 + ⋯ - ⋯ - Wikipedia

   en.wikipedia.org/wiki/1_%2B_2_%2B_3_%2B_4_%2B_%E...

   The partial sums of the series 1 + 2 + 3 + 4 + 5 + 6 + ⋯ are 1, 3, 6, 10, 15, etc.The nth partial sum is given by a simple formula: = = (+). This equation was known ...

5. 1-planar graph - Wikipedia

   en.wikipedia.org/wiki/1-planar_graph

   The bound of 4n − 8 on the maximum possible number of edges in a 1-planar graph can be used to show that the complete graph K 7 on seven vertices is not 1-planar, because this graph has 21 edges and in this case 4n − 8 = 20 < 21. [7] A 1-planar graph is said to be an optimal 1-planar graph if it has exactly 4n − 8 edges, the maximum possible.

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