Utility Graph
The utility problem asks, ``Can a Planar Graph be constructed from each of three nodes (`house owners') to each ofthree other nodes (`wells')?'' The answer is no, and the proof can be effected using the Jordan Curve Theorem,while a more general result encompassing this one is the Kuratowski Reduction Theorem. The utility graph 
is the graph showing the relationships described above. It is identical to the Thomsen Graph and, in the moreformal parlance of Graph Theory, is known as the Complete Bipartite Graph 
.
References
Chartrand, G. ``The Three Houses and Three Utilities Problem: An Introduction to Planar Graphs.'' §9.1 in Introductory Graph Theory. New York: Dover, pp. 191-202, 1985. Ore, Ø. Graphs and Their Uses. New York: Random House, pp. 14-17, 1963. Pappas, T. ``Wood, Water, Grain Problem.'' The Joy of Mathematics. San Carlos, CA: Wide World Publ./Tetra, pp. 175 and 233, 1989.
- MacMahon's Prime Number of Measurement
- MacRobert's E-Function
- Madelung Constants
- Maeder's Owl Minimal Surface
- Maehly's Procedure
- Magic Circles
- Magic Constant
- Magic Cube
- Magic Geometric Constants
- Magic Graph
- Magic Hexagon
- Magic Labeling
- Magic Number
- Magic Series
- Magic Square
- Magic Star
- Magic Tour
- Mahler-Lech Theorem
- Mahler's Measure
- Mainardi-Codazzi Equations
- Majorant
- Major Axis
- Major Triangle Center
- Makeham Curve
- Malfatti Circles