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Digital metrics: A graph-theoretical approach

Harary, Frank; Melter, Robert A.; Tomescu, Ioan

Harary, Frank; Melter, Robert A.; Tomescu, Ioan

1984-03

Citation:Harary, Frank, Melter, Robert A., Tomescu, Ioan (1984/03)."Digital metrics: A graph-theoretical approach." Pattern Recognition Letters 2(3): 159-163. <http://hdl.handle.net/2027.42/24881>

Abstract: Consider the following two graphs M and N, both with vertex set Z x Z, where Z is the set of all integers. In M, two vertices are adjacent when their euclidean distance is 1, while in N, adjacency is obtained when the distance is either 1 or [radical sign]2. By definition, H is a metric subgraph of the graph G if the distance between any two points of H is the same as their distance in G. We determine all the metric subgraphs of M and N. The graph-theoretical distances in M and N are equal respectively to the city block and chessboard matrics used in pattern recognition.