The average or mean of the distances between pairs of vertices in a connected graph is a natural measure of the compactness of that graph. Using graphs to represent shapes, or corridor arrangements, we arrive, through a limiting process, at a concept for mean distance in shapes. This paper gives the mean distance for eight specific shapes and six infinite families of shapes.
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References
1.
DoyleJ KGraverJ E, 1977“Mean distance in a graph”Discrete Mathematics17147–154
2.
DoyleJ KGraverJ E, 1982“Mean distance for shapes”Journal of Graph Theory (forthcoming)
3.
MarchLSteadmanP, 1971The Geometry of Environment (Royal Institute of British Architects, London)
