A Note On Some Domination Parameters in Graph Products

In this paper, we study the domination number, the global dom ination number, the cographic domination number, the global co graphic domination number and the independent domination number of all the graph products which are non-complete extended p-sums (NEPS) of two graphs.

Structure Absorption Spectra Correlation in a Series of 2,6-Dimethyl-4-arylpyrylium Salts

A combined experimental and theoretical study of the absorption spectra of a group of closely related pyrylium perchlorates 1-11 are presented. Minor changes in the position of the substituents lead to drastic changes in the absorption spectra in this series of compounds. We have attempted to explain the observed changes using the x,y-band notation developed by Balaban and co-workers. Absorption spectra of all compounds are compared with results from time-dependent density functional theory (TDDFT) and Zerner’s intermediate neglect of differential overlap (ZINDO/S) level calculations. Results of the calculations are in good agreement with experimental observations and an interesting correlation between Balaban’s notations and the MO transitions are obtained for simple derivatives. It is suggested that for more complex systems such as R- and â-naphthyl substituted systems, the empirical method is not appropriate.

The P3 Intersection Graph

We define a new graph operator called the P3 intersection graph, P3(G)- the intersection graph of all induced 3-paths in G. A characterization of graphs G for which P-3 (G) is bipartite is given . Forbidden subgraph characterization for P3 (G) having properties of being chordal , H-free, complete are also obtained . For integers a and b with a > 1 and b > a - 1, it is shown that there exists a graph G such that X(G) = a, X(P3( G)) = b, where X is the chromatic number of G. For the domination number -y(G), we construct graphs G such that -y(G) = a and -y (P3(G)) = b for any two positive numbers a > 1 and b. Similar construction for the independence number and radius, diameter relations are also discussed.

The Edge C4 Graph of a Graph

Abstract. The edge C4 graph E4(G) of a graph G has all the edges of Gas its vertices, two vertices in E4(G) are adjacent if their corresponding edges in G are either incident or are opposite edges of some C4. In this paper, characterizations for E4(G) being connected, complete, bipartite, tree etc are given. We have also proved that E4(G) has no forbidden subgraph characterization. Some dynamical behaviour such as convergence, mortality and touching number are also studied

GALLAI AND ANTI-GALLAI GRAPHS OF A GRAPH

Abstract. The paper deals with graph operators-the Gallai graphs and the anti-Gallai graphs. We prove the existence of a finite family of forbidden subgraphs for the Gallai graphs and the anti-Gallai graphs to be H-free for any finite graph H. The case of complement reducible graphs-cographs is discussed in detail. Some relations between the chromatic number, the radius and the diameter of a graph and its Gallai and anti-Gallai graphs are also obtained.

Raman spectra of polymethyl methacrylate optical fibres excited by a 532 nm diode pumped solid state laser

Polymethyl methacrylate (PMMA) optical fibres are fabricated by a preform drawing process. The Raman spectra of PMMA fibres are recorded using a diode pumped solid state laser emitting at 532 nm and a CCD-spectrograph in the 400–3800 cm−1 range. The variation of the Raman intensity with the length of the optical fibre is studied. Investigations are carried out on the variation of FWHM of the Raman peak at 2957 cm−1 with the length of the optical fibre and pump power. The differential scattering cross section and gain coefficient of the Raman peak at 2957 cm−1 in PMMA are calculated in relation to that of toluene.

Raman spectra of polymethyl methacrylate optical fibres excited by a 532 nm diode pumped solid state laser

Polymethyl methacrylate (PMMA) optical fibres are fabricated by a preform drawing process. The Raman spectra of PMMA fibres are recorded using a diode pumped solid state laser emitting at 532 nm and a CCD-spectrograph in the 400–3800 cm−1 range. The variation of the Raman intensity with the length of the optical fibre is studied. Investigations are carried out on the variation of FWHM of the Raman peak at 2957 cm−1 with the length of the optical fibre and pump power. The differential scattering cross section and gain coefficient of the Raman peak at 2957 cm−1 in PMMA are calculated in relation to that of toluene

Studies on some graph operators and related topics

Department of Mathematics, Cochin University of Science and Technology

NIR to UV absorption spectra and the optical constants of phthalocyanines in glassy medium

Optical absorption studies of phthalocyanines (Pc-s) in borate glass matrix have been reported for the first time. Measurements have been done corresponding to photon energies between 1.1 and 6.2 eV for free base, manganese, iron, nickel, molybdenum, cobalt and copper phthalocyanines. Several new discrete transitions are observed in the UV–vis region of the spectra in addition to a strong continuum component of absorption in the IR region. Values of some of the important optical constants viz. absorption coefficient (α), molar extinction coefficient (ε), absorption cross-section (σa), band width (Δλ), electric dipole strength (q2) and oscillator strength (f) for the relevant electronic transitions are also presented. All the data reported for Pc-s in the new matrix have been compared with those corresponding to solution, vapor and thin film media.

Overtone Spectra of 1,2-Dichloro-And Dibromo-Ethanes in the Near Infrared Region

The vibrational overtone spectra 0f the liquid phase 1,2-dichloroethane and 1,2-dibromoethane in the spectral regions of CH stretching local mode overtones corresponding to delta v CH= = 2 to delta v CH=5 are reported. The observed spectral features are assigned using the local mode model. LocaI mode frequencies WCH and diagonal local mode anharmonicities XCH are obtained from an analysis of the spectra. The local-local combinations observed are interpreted on the basis of a coupled CH oscillator model hamiltonian. Local-normal combinations show complex structures and their possible assignments are given.

Overtone spectra of styrene and polystyrene in the visible and near infrared regions

Vibrational overtone spectra of styrene (liquid) and polystyrene (solid), studied by the laser-induced thermal lens (for ΔV=6) and the conventional near infrared absorption (for ΔV=3–5) techniques, are reported. For polystyrene, the overtone energy-bond length correlation predicts that the aryl CH bonds are ∼0.0005 Å longer than that in benzene, while no such conclusions could be drawn on styrene. Thesp 3 CH overtones in polystyrene are observed on the low energy side of the aryl CH overtones.

Studies on Some Graph Classes

Department of Mathematics, Cochin University of Science and Technology