Graph theory itself is typically dated as beginning with Leonhard Euler`s 1736 work on the Seven Bridges of Königsberg. However, drawings of complete graphs, with their vertices placed on the points of a regular polygon, appeared already in the 13th century, in the work of Ramon Llull. Such a drawing is sometimes referred to as a mystic rose. ==....
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http://en.wikipedia.org/wiki/Complete_graph
(from the article `combinatorics`) A complete graph is a graph with vertices, any two of which are adjacent. The line graph of a graph is a graph the vertices of which correspond ... ...13A), the resulting figure is a graph; the points, or corners, are called the vertices, and the lines are called the edges. If every pair of ... ...
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http://www.britannica.com/eb/a-z/c/121
A connected graph in which exactly one edge connects each pair of vertices. A complete graph with n vertices, denoted K
n, has n(n - 1)/2 edges (i.e. the nth triangular number), (n-1)! Hamilton circuits, and a chromatic number of n. Every vertex in K
n has...
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http://www.daviddarling.info/encyclopedia/C/complete_graph.html
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