Showing papers on "Planarity testing published in 1983"
TL;DR: In this article, the NH 2 -inversion levels in the A 1 B 2 State of aniline-NH 2 and -ND 2 have been improved using new information regarding
87 citations
TL;DR: In this article, a precise analysis of the 1H nmr spectrum of 1,2-dimethoxybenzene in benzene solution yields an accurate value for the proximate spin-spin coupling constant,, between the ortho ring proton and the...
Abstract: A precise analysis of the 1H nmr spectrum of 1,2-dimethoxybenzene in benzene solution yields an accurate value for the proximate spin–spin coupling constant, , between the ortho ring proton and the...
33 citations
TL;DR: A program which implements the proposed algorithms for routing nets inside an arbitrarily shaped region has been written and tested and the results from this program are shown as examples.
Abstract: In this paper we present a discussion of planarity testing and detailed single-layer routing. A program which implements the proposed algorithms for routing nets inside an arbitrarily shaped region has been written and tested. The results from this program are shown as examples.
32 citations
TL;DR: In this article, the structures and conformations of cyclopentane and cyclohexene have been investigated using SCF gradient ab initio computation with a double zeta basis set, and the half-chair (C2) and the envelope (Cs) forms were found to be isoenergetic.
Abstract: The structures and conformations of cyclopentane, cyclopentene, and cyclopentadiene have been investigated by SCF gradient ab initio computation with a double zeta basis set. For cyclopentane the half-chair (C2) and the envelope (Cs) forms were found to be isoenergetic, consistent with the experimentally observed free pseudorotation. The barrier to coplanarity of the ring is 4.3 kcal mol−1. Cyclopentene has a puckered Cs equilibrium conformation with a very low barrier to planarity. Cyclopentadiene has a planar ring. The compounds with 5, 3 and 1 methylene groups, respectively, show a decreasing tendency to form puckered rings as interaction between adjacent methylene groups becomes of less significance compared with the influence of angle strain which favors ring planarity. A corrected geometrical optimization of the half-boat (Cs) form of cyclohexene is also presented.
30 citations
TL;DR: An algorithm is described which accepts as input the edges of a convex polyhedron, listed in any order, and which produces a consistent collection of sequences of points which describe the faces of thepolyhedron as required by certain display rendering packages.
22 citations
TL;DR: In this paper, a study of the Raman intensities of benzene in series of styrene, biphenyl and stilbene hydrocarbons is reported, and it is shown that after correction for the resonance Raman effect, the intensities can be related to the degree of planarity of the molecules via a previously derived relationship between the intensity and the length of the conjugated system.
Abstract: A study of the Raman intensities of ν8 mode of benzene in series of styrene, biphenyl and stilbene hydrocarbons is reported. It is shown that, after correction for the resonance Raman effect, the intensities can be related to the degree of planarity of the molecules via a previously derived relationship between the intensity and the length of the conjugated system.
17 citations
TL;DR: The molecular structures of a variety of 1, 5-diazabicyclo[3.3.0] octadienediones, including three 9, 10-dioxa-syn-bimanes, three 4, 6-bridged 9-10-decodabimanes and three 9 and 10-deconditioned anti-deconvariant bimanes were analyzed and compared with respect to planarity, bond distances, bond angles and intermolecular packing as mentioned in this paper.
12 citations
TL;DR: The far-infrared spectra in the region of 50-450 cm-' are reported for the vapours of cyclohexanone and the structurally related compounds tetrahydro-4H-pyran-4-one, tetrahedro- 4H-thiopyran -4-1, 4H pyran 4-1.5, and 4H polygonal-4.1.1 as discussed by the authors, which are characterized by two or in some cases three sequences of Q branches.
Abstract: The far-infrared spectra in the region of 50-450 cm-' are reported for the vapours of cyclohexanone and the structurally related compounds tetrahydro-4H-pyran-4-one, tetrahydro-4H-thiopyran-4-one. tetrahydro-4H-pyran-3-one, 1,3-dioxan-5one, and 4H-pyran-4-one. Except for the last mentioned, the spectra are characterized by two or in some cases three sequences of Q branches which are assigned to the out-of-plane deformations of the cyclohexanone ring. The lowest wavenumber sequence in each compound is believed to arise from a vibration which, if completely executed, would take the chair conformation to its equivalent via an inversion through the planar form. Each sequence is amenable to solution by a one-dimensional Hamiltonian incorporating a quadratic-quartic potential function, providing estimates for the magnitudes of the barriers to planarity.
10 citations
TL;DR: In this paper, the authors discuss the edge-reconstruction of planar graphs that triangulate surfaces and show that all 4-connected graphs are edge-hardened.
Abstract: Publisher Summary This chapter discusses two kinds of graphs having certain topological properties. The chapter discusses the way all 4-connected planar graphs are edge-reconstructible. The chapter also discusses the edge-reconstruction of certain graphs that triangulate surfaces. There are two reconstruction techniques to establish the results. The conditions of 4-connectedness and planarity allow us to make heavy use of embedding properties and of Kuratowski's characterization of planar graphs. In general, these are no longer available for surfaces of higher genera.
5 citations
01 Jan 1983
TL;DR: In this paper, the authors present a survey of the mathematical content of some results of planar graphs and their application in the analysis and synthesis of electric networks, while relations of planarity to layout design of printed circuit board etc.
Abstract: Planarity, and the strongly realted concept of duality of planar graphs, have been the sources of many investigations in the last five decades, not only in combinatorics but in electrical engineering as well. Recently some engineering research communities have found new results on these topics. The present paper is an attempt to discuss the mathematical content of some results of this type. (The motivation of all these applications is more or less related to the analysis and synthesis of electric networks, while relations of planarity to layout design of printed circuit board etc. is disregarded.) The survey is intended for mathematicians; no engineering background is required.
2 citations
01 Jan 1983