### Table 3. Algebraic connectivity of connected graphs on six vertices

"... In PAGE 4: ... Paper n5b55n5d provides pictures of the 509 cubic graphs on fourteen vertices and some non-spectral data. Table3 in n5b24n5d, based on n5b5n5d, contains connected cubic graphs with up to 12 vertices. The pictures, spectrum and coen0ecients of the characteristic polynomials are included.... In PAGE 9: ... Table 2 contains algebraic connectivities for graphs in Table 1. Table3 refers to the table of 112 connected graphs on six vertices from n5b29n5d which is described in Section 1. Using identin0ccation numbers of graphs from n5b29n5d we give algebraic connectivities of the 112 connected graphs.... ..."

### Table 13: The operators of the computer domain.

1994

"... In PAGE 51: ... Similarly, for it to be plugged in the device must be located with the reachofapower outlet. Table13 shows the operators for this domain. For this domain, Alpine generates the graph shown in Figure 10.... ..."

Cited by 5

### Table 5. Laws for Commuting and Distributing Update Connectives

2006

"... In PAGE 55: ...Schema Variables Table5 . Modi ers for Schema Variables Modi er Applicable to rigid \term A \formula Terms or formulae that can syntactically be identi ed as rigid strict \term A Terms of type A (and not of proper subtypes of A) list \program t Sequences of program entities.... In PAGE 106: ...xample 2. We continue Example 1 and assume the same vocabulary/algebra. a := 1 ; f(a) := 2 a := 1 j f(1) := 2 valS; (a := 1 ; f(a) := 2) = fhai 7! 1; hf; (1)i 7! 2g valS; (a := 1 ; (a := 3 j f(a) := 2)) = fhai 7! 3; hf; (1)i 7! 2g We normalise the update in the second line using the given rewriting rules: a := 1 ; (a := 3 j f(a) := 2) (R45) ! a := 1 j fa := 1g (a := 3 j f(a) := 2) (R48) ! a := 1 j (fa := 1g a := 3 j fa := 1g f(a) := 2) (R47) ! a := 1 j (a := fa := 1g 3 j f(fa := 1g a) := fa := 1g 2) (R2); (R12) ! a := 1 j (a := 3 j f(non-rec(a := 1; a; ())) := 2) (R11) ! a := 1 j (a := 3 j f(if true then 1 else a) := 2) The last expression can be simpli ed further using rules for conditional terms, which are, however, beyond the scope of this paper. Further, using (R54) in Table5 , it is possible to eliminate the assignment a := 1, which is overridden by a := 3. 8 Soundness and Completeness of Update Application The following two lemmas state that the rewriting rules from Sect.... In PAGE 111: ...ewriting rules for update application (than the ones given in Sect. 5). This has been done for the implementation of updates in KeY. Table5 gives, besides others, identities that enable to establish form (1) by turning sequential composition into parallel composition, distributing if and for through parallel composition and commuting if and for. Another impor-... ..."

### Table 1: BNA: Basic network algebra .

"... In PAGE 5: ...g. axiom B10 in Table1 ) and notational convenience it is useful to use the block extensions of the feedback and of the above constants. Their meaning may be obtained using the identities in axioms R5{R6 and B6, B8{B9, A12{A19, respectively.... In PAGE 6: ... The algebraic structure de ned by the BNA axioms was introduced in [Ste86, CaS88 amp;89] under the name of bi ow; in the more sistematic notation used in [Ste94] it is also called a -ssmc with feedback.2 The algebraic structure de ned by axioms B1{B10 in Table1 and A1{A19 in Table 2 was introduced in [CaS91] under the name d -ssmc. Finally, the algebraic structure de ned by all the axioms in Tables 1 and 2 is called d -ssmc with feedback, cf.... In PAGE 6: ... [Ste86, CaS88 amp;89]. Correctness: Using the graphical interpretation of the operations and of the constants it is easy to see that the axioms in Table1 are correct with respect to graph isomorphism equivalence.... ..."

### Table 2: Number of in the connectivity graphs

1992

"... In PAGE 8: ... The scanning is an operation of order O#28dn#29 and, for the examples in Figure 2, takes about #0Cve seconds on a DECstation 5000. Table2 gives the number of arcs in the connectivity graphs and the average number of connections per cell. As can be seen, the number of connections is low and appears to be a result of the typical size distribution of slippery cells.... ..."

Cited by 15

### Table 1: Specializations of Network Design Problems with Connectivity Constraints

1999

"... In PAGE 6: ... In this application each node v in the graph has a connectivity requirement r and the connectivity require- ments between nodes s and t are given by rt = min{r, rt}. Table1 shows several other noteworthy cases of the NDC problem. A few observations concerning the entries in Table 1 are worth making.... In PAGE 6: ... Table 1 shows several other noteworthy cases of the NDC problem. A few observations concerning the entries in Table1 are worth making. The k-edge dis- joint path problem seeks, at minimum cost, k-edge disjoint paths between specified nodes s and t.... In PAGE 8: ...s a unitary NDC problem. Otherwise, it is a nonunitary NDC problem. For example, the SND problem is a unitary NDC problem, while the general Steiner forest problem is a nonunitary NDC problem. The examples in Table1 show that the NDC problem models a very wide variety of con- nectivity problems on graphs. These problems appear both as stand alone problems and as subproblems in more complex network design applications (like VLSI design and telecom- munications network design and management).... ..."

Cited by 6

### Table 1: Specializations of Network Design Problems with Connectivity Constraints

1999

"... In PAGE 2: ... In this application each node v in the graph has a connectivity requirement rv and the connectivity requirements be- tween nodes s and t are given by rst = minfrs; rtg. Table1 shows several other noteworthy cases of the NDC problem. A few observations concerning the entries in Table 1 are worth making.... In PAGE 2: ... Table 1 shows several other noteworthy cases of the NDC problem. A few observations concerning the entries in Table1 are worth making. The k-edge dis- joint path problem seeks, at minimum cost, k-edge disjoint paths between specified nodes s and t.... In PAGE 4: ...s a unitary NDC problem. Otherwise, it is a nonunitary NDC problem. For example, the SND problem is a unitary NDC problem, while the general Steiner forest problem is a nonunitary NDC problem. The examples in Table1 show that the NDC problem models a very wide variety of con- nectivity problems on graphs. These problems appear both as stand alone problems and as subproblems in more complex network design applications (like VLSI design and telecom- munications network design and management).... ..."

Cited by 6

### Table 4. Networks and their Application

"... In PAGE 11: ... Many network types are needed to fulfill the dream of cyberspace and the information superhighway. Several important ones are listed in Table4 . Figure 2 shows the change in bandwidth of two important communication links that are the basis of Wide Area Networks and the connection to them.... ..."

### Table 1: An overview of connected graph searching

"... In PAGE 11: ...roperty 1 Let G be the graph depicted on Fig. 6. We have cvs(G) = 4 and any winning monotone connected visible search strategy for G uses at least 5 searchers. 4 Conclusion A quick glance at Table1 indicates that our results combined with the previous results in this field let only one problem to be solved, as far as connected search is concerned. Namely: is the bound on the left hand side of Equation 1, i.... ..."