### Table 2: Summary of growth constants, typical properties, and limit laws for unlabeled and labeled dissections and outerplanar graphs.

2007

"... In PAGE 21: ...6. 6 Concluding remarks A summary of the estimated growth constants and other parameters for unlabeled outer- planar graphs is presented in Table2 . For comparison we also include the corresponding labeled quantities derived in [4].... ..."

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### Table 1: Optimal upper bounds for the clique number, inductiveness, and chromatic number of the square of a chordal / non-chordal outerplanar graph G.

2004

"... In PAGE 4: ... We examine in detail the low-degree cases, lt; 7, and derive best possible upper bounds on the maximum clique and chromatic numbers, as well as inductiveness of squares of outerplanar graphs. These bounds are illustrated in Table1 . We treat the special case of chordal outerplanar graphs separately, and further classify all chordal outerplanar graphs G for which the inductiveness of G2 exceeds or the clique or chromatic number of G2 exceed + 1.... In PAGE 17: ...orollary 4.10 together with Theorems 4.3 and 4.5 complete the proof of Theorem 4.1 as well as the entries in Table1 in the chordal case for 2 f2; 3; 4; 5; 6g. Observation 4.... ..."

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### Table 1 summarizes the characterization results about the -drawability of outerplanar graphs. The entries having a bibliographic reference describe previously known results. All other entries describe results from this paper. fCOg, fBOg, and fMOg are the set of all connected outerplanar, biconnected outerplanar, and maximal outerplanar graphs, respectively. GCO( ), GBO( ), and GMO( ) are the classes of connected outerplanar, bicon- nected outerplanar, and maximal outerplanar ( )-drawable graphs, respectively. Similarly, GCO[ ], GBO[ ], and GMO[ ] are the classes of connected outerplanar, biconnected outerplanar, and maximal outerplanar [ ]-drawable graphs, respectively. Gk denotes the class of graphs such that the number of biconnected components sharing a cut-vertex is at most k; Tk is the class of trees whose vertex degree is at most k; T is the class of forbidden trees described in [3].

"... In PAGE 5: ... Table1 : Summarizing the characterization results on the -drawability of outerplanar graphs for 1 2. 2 Preliminaries We review rst standard de nitions on outerplanar graphs.... ..."

### Table 1 summarizes the characterization results about the -drawability of outerplanar graphs. The entries having a bibliographic reference describe previously known results. All other entries describe results from this paper. fCOg, fBOg, and fMOg are the set of all connected outerplanar, biconnected outerplanar, and maximal outerplanar graphs, respectively. GCO( ), GBO( ), and GMO( ) are the classes of connected outerplanar, bicon- nected outerplanar, and maximal outerplanar ( )-drawable graphs, respectively. Similarly, GCO[ ], GBO[ ], and GMO[ ] are the classes of connected outerplanar, biconnected outerplanar, and maximal outerplanar [ ]-drawable graphs, respectively. Gk denotes the class of graphs such that the number of biconnected components sharing a cut-vertex is at most k; Tk is the class of trees whose vertex degree is at most k; T is the class of forbidden trees described in [3].

"... In PAGE 4: ... Table1 : Summarizing the characterization results on the -drawability of outerplanar graphs for 1 2. 2 Preliminaries We review rst standard de nitions on outerplanar graphs.... ..."

### Table 1 summarizes the characterization results about the -drawability of outerplanar graphs. The entries having a bibliographic reference describe previously known results. All other entries describe results from this paper. fCOg, fBOg, and fMOg are the sets of all connected outerplanar, biconnected outerplanar, and maximal outerplanar graphs, respectively. GCO( ), GBO( ), and GMO( ) are the classes of connected outerplanar, bicon- nected outerplanar, and maximal outerplanar ( )-drawable graphs, respectively. Similarly, GCO[ ], GBO[ ], and GMO[ ] are the classes of connected outerplanar, biconnected outerplanar, and maximal outerplanar [ ]-drawable graphs, respectively. Gk denotes the class of graphs such that the number of biconnected components sharing a cut-vertex is at most k; Tk is the class of trees whose vertex degree is at most k; T is the class of forbidden trees described in [2].

"... In PAGE 2: ... Table1 : Summarizing the characterization results on the -drawability of outerplanar graphs for 1 2. References [1] P.... ..."

### Table 1: Optimal upper bounds for the clique number, inductiveness, and chromatic number of the square of a chordal / non-chordal outerplanar graph G.

### Table 7.3 summarizes the characterization results about the fl-drawability of outerplanar graphs that can be found in [LS93, LL96b]. All other entries describe results from this paper. CO, BO, and MO are the set of all connected outerplanar, biconnected outerplanar, and maximal outerplanar graphs, respectively. GCO(fl), GBO(fl), and GMO(fl) are the classes of connected outerplanar, biconnected outerplanar, and maximal outerplanar (fl)-drawable graphs, respectively. Similarly, GCO[fl], GBO[fl], and GMO[fl] are the classes of connected outerplanar, biconnected outerplanar, and maximal outerplanar [fl]-drawable graphs, re- spectively. Gk denotes the class of graphs such that the number of biconnected components sharing a cut-vertex is at most k.

### Table 3 show the outerplanar crossing number of some complete p-partite graphs. It can be seen that the results of the graphs tested by the model with both energy functions are close to the optimal values, but can still be improved.

"... In PAGE 6: ...Table3 : Outerplanar crossing numbers of Kn(p) tested with the neural network model with difierent energy functions Graphs 1(E1) 1(E2) Opt. K3(2) 3 3 3 K4(2) 16 19 16 K5(2) 54 54 50 K3(3) 54 56 54 K4(3) 224 226 216 K5(3) 628 617 600 K3(4) 290 286 279 K4(4) 1045 1066 1024 For energy function 1 (E1), the number of iterations (N1) varies with difierent tests, while the number of iterations (N2) for energy function 2 (E2) keeps nearly same for every test, but usually N1 lt; N2 .... ..."

### Table 2 Clustering coeSOcients of the market graph

2004

### Table 1: Event probabilities for causal structures Event Graph 0 Graph 1 Graph 2

2004

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