Total Face Irregularity Strength of Type (Alpha, Beta, Gamma) of Grid Graphs

We investigate new graph characteristics namely total (vertex, edge) face irregularity strength of gen- eralized plane grid graphs Gmn under k-labeling Phi of type (Alpha, Beta, Gamma). The minimum integer k for which a vertex-edge labelled graph has distinct face weights is called the total face irregularity strength of the graph and is denoted by tfs(Gmn). In this article, the graphs G = (V;E; F) under consideration are simple, finite, undirected and planar. We will estimate the exact tight lower bounds for the total face irregularity strength of some families of generalized plane grid graphs.

Total Face Irregularity Strength of Type (Alpha, Beta, Gamma) of Grid Graphs

We investigate new graph characteristics namely total (vertex, edge) face irregularity strength of gen- eralized plane grid graphs Gmn under k-labeling Phi of type (Alpha, Beta, Gamma). The minimum integer k for which a vertex-edge labelled graph has distinct face weights is called the total face irregularity strength of the graph and is denoted by tfs(Gmn). In this article, the graphs G = (V;E; F) under consideration are simple, finite, undirected and planar. We will estimate the exact tight lower bounds for the total face irregularity strength of some families of generalized plane grid graphs.

Numerical simulation of fast atmospheric pressure discharge in gas diode with plane-grid cathode system

In this paper we perform an accurate time-dependent finite-element numerical gas discharge simulation in two-dimensional semi-periodic computational geometry of the gas diode with a plane-grid cathode system. The diode configuration we investigate is similar to previously studied experimentally. Discharge simulation is performed in the framework of two-moment macroscopic (hydrodynamic) discharge plasma model accounting photoionization and autoelectronic emission from nonuniform electrodes surfaces. The results of numerical calculations can be used for further estimations of a runaway electron flows characteristics.

Micro Layout Research of Reclamation Area Based on Plane Grid Topology Formation

The micro-layout research of the reclamation area involves many other areas and disciplines, occupies an important position in the coastal economic study. On the base of geometry theory, this paper puts the micro-layout of the reclamation area under the economic analysis within the formation of two-dimensional plane of the grid point topology. Here we take the Heishijiao coastal areas of Dalian as the example for micro layout of the reclamation area research within the two-dimensional plane variable framework, which is calculated by the Ising lattice model. For the better macroeconomic development in the area as the objective function, the maximum economic value will determine the optimal layout. The results show that, in coastal reclamation area it should not be paid too much notation to the width of the extension in the sea, and more reclamation area should be gathered to the city's prosperity zone reflected in the overall layout of layering.