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<p><b>Abstract</b>—This paper investigates the influence of the cost function on the optimal match between two graphs. It is shown that, for a given cost function, there are an infinite number of other cost functions that lead, for any given pair of graphs, to the same optimal error correcting matching. Furthermore, it is shown that well-known concepts from graph theory, such as graph isomorphism, subgraph isomorphism, and maximum common subgraph, are special cases of optimal error correcting graph matching under particular cost functions.</p>
Graph, subgraph, maximum common subgraph, graph isomorphism, subgraph isomorphism, graph matching, error correcting graph matching, cost function, edit operation, graph edit distance.

H. Bunke, "Error Correcting Graph Matching: On the Influence of the Underlying Cost Function," in IEEE Transactions on Pattern Analysis & Machine Intelligence, vol. 21, no. , pp. 917-922, 1999.
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