International Journal of Combinatorics / 2012 / Article / Tab 1

Research Article

A Convex Relaxation Bound for Subgraph Isomorphism

Table 1

List of all outcomes of the structure comparison term when two different nodes and of graph are mapped to two different nodes and in the second graph . The first column describes the relation between the concerned nodes and the last column shows the associated cost . Only in cases I and IV is the structure preserved and can lead to an isomorphism. No cost is added in this cases. The other cases (II and III) do not preserve the structure and result in a total cost larger than 0. For details see the text.

Node configurations Cost

I: , adjacent; , adjacent 1 0 0 1 0
II: , adjacent; , not adjacent 1 1 0 0 1
III: , not adjacent; , adjacent 0 0 1 1 1
IV: , not adjacent; , not adjacent 0 1 1 0 0

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