### Table 2. Experimental Results on the Subgraph Isomorphism Problem

"... In PAGE 13: ... We randomly generated instances of the problem using parameters d1 and d2 that are densities of G1 and G2, respectively. The results are collected in Table2 . The meaning of columns is the same except the parameters of the problem.... ..."

### Table 2. Number of solutions and time in seconds (Ullmann approach) and number of solutions, BDD size in number of nodes, and time in seconds (BDD approach) taken to nd all subgraph isomorphisms of a random graph with m vertices into a random graph with n vertices, both with 25% connectivity.

"... In PAGE 9: ... For each generated pattern and target random graphs, the Boolean matrix of the pattern has been added to the Boolean matrix of the target and non-connected graphs have been discarded, as was already done in [21]. Table2 shows statistics for the approach by Ullmann (number of solutions and time in seconds) and the BDD approach (number of solutions, size of the BDD containing them, and time in seconds) for nding all subgraph isomorphisms of a random pattern graph into a random target graph, both with arc probability 25%. For each variable the mean and the standard deviation, which have been estimated over a sample of 50 observations, are given.... ..."

### Table 2. Number of solutions and time in seconds (Ullmann approach) and number of solutions, BDD size in number of nodes, and time in seconds (BDD approach) taken to find all subgraph isomorphisms of a random graph with m vertices into a random graph with n vertices, both with 25% connectivity.

"... In PAGE 9: ... For each generated pattern and target random graphs, the Boolean matrix of the pattern has been added to the Boolean matrix of the target and non-connected graphs have been discarded, as was already done in [21]. Table2 shows statistics for the approach by Ullmann (number of solutions and time in seconds) and the BDD approach (number of solutions, size of the BDD containing them, and time in seconds) for finding all subgraph isomorphisms of a random pattern graph into a random target graph, both with arc probability 25%. For each variable the mean and the standard deviation, which have been estimated over a sample of 50 observations, are given.... ..."

### Table 6. Subsumption run time in subgraph isomorphism family

2004

"... In PAGE 17: ... The clause is a randomly generated graph with n nodes and 3n edges, and the example is the same set plus 3n extra edges. The results for n = 10 are given in Table6 . Deterministic tables fail for values of n larger than 8 and are omitted.... In PAGE 17: ... Deterministic tables fail for values of n larger than 8 and are omitted. As can be seen Django works very well in this case and randomized tables work well even with small parameters, and both table size and repeats (marked with TH and R in Table6 , resp.) are efiec- tive in increasing the performance of the randomized tests.... ..."

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### Table 5. Comparison with the error-correcting sub-graph isomorphism algorithm

2002

"... In PAGE 5: ... This can be very significant when matching large graphs. Table5 shows a comparison with the A*- based error-correcting algorithm over 1000 pairs of graphs generated randomly. The size of each graph is between 2 and 10 nodes.... ..."

Cited by 2

### Table 1: Subgraph isomorphism problem: complexity for a xed pattern H and for an input graph restricted to some class of graphs.

### Table 1. Number of solutions, BDD size in number of nodes, and time in seconds taken to nd all subgraph isomor- phisms of a random graph with m vertices into a random graph with n vertices, both with 25% connectivity.

"... In PAGE 8: ... A total of 384 experiments have been carried out, for di erent values of pattern arc probability (10%, 15%, 20%, and 25%), target arc probability (10%, 15%, 20%, and 25%), pattern size (3, 4, 5, and 6 vertices), and target size (10, 25, 50, 100, 150, and 200 vertices). Table1 shows statistics for the number of solutions, the size of the BDD containing them, and the time (in seconds) taken to nd all subgraph isomorphisms of a random pattern graph into a random target graph, both with arc probability 25%. In order to compare the BDD approach to the results reported in [21], where non-directed graphs are... ..."

### Table 1. Number of solutions, BDD size in number of nodes, and time in seconds taken to find all subgraph isomor- phisms of a random graph with m vertices into a random graph with n vertices, both with 25% connectivity.

"... In PAGE 8: ... A total of 384 experiments have been carried out, for different values of pattern arc probability (10%, 15%, 20%, and 25%), target arc probability (10%, 15%, 20%, and 25%), pattern size (3, 4, 5, and 6 vertices), and target size (10, 25, 50, 100, 150, and 200 vertices). Table1 shows statistics for the number of solutions, the size of the BDD containing them, and the time (in seconds) taken to find all subgraph isomorphisms of a random pattern graph into a random target graph, both with arc probability 25%. In order to compare the BDD approach to the results reported in [21], where non-directed graphs are... ..."

### Table 1 Relationship between cohesiveness of subgraph patterns and the probability

2006

"... In PAGE 6: ...common substrates divided by the number of all sub- graphs. As shown in Table1 , all three constituents of 3.6% of triad 1 are the common substrates, whereas all three constituents of 36.... ..."

### Table 1 Non-isomorphic imbeddings of isomorphic star complements arise in case n288n29, as can

"... In PAGE 6: ... In this example, it turns out that for isomorphic star complements, the subgraphs induced by the corresponding star cells are always isomorphic, but this statement is not true in general n28see n5b1, Section 1n5dn29. The star complements n281n29n7bn2811n29 are presented in Table1 , where column 1 contains the identin0cca- tion number, column 2 gives the largest eigenvalue, column 3 gives the number of mutually isomor- phic star complements in each case, and column 4 gives the number of edges in the corresponding star cells. The star complements n285n29 and n286n29, which have the same largest eigenvalue n28or indexn29, are dis- tinguished by the second largest eigenvalue n28given in parenthesesn29, but the star complements n283n29 and n284n29 are cospectral.... ..."