On Topological Indices for New Classes of Benes Network

Topological indices (TIs) transform a molecular graph into a number. The TIs are a vital tool for quantitative structure activity relationship (QSAR) and quantity structure property relationship (QSPR). In this paper, we constructed two classes of Benes network: horizontal cylindrical Benes network HCB r and vertical cylindrical Benes network obtained by identification of vertices of first rows with last row and first column with last column of Benes network, respectively. We derive analytical close formulas for general Randić connectivity index, general Zagreb, first and the second Zagreb (and multiplicative Zagreb), general sum connectivity, atom-bond connectivity ( VCB r ), and geometric arithmetic ABC index of the two classes of Benes networks. Also, the fourth version of GA and the fifth version of ABC indices are computed for these classes of networks.

Design and Implementation of Rearrangable Non-Blocking Switching Network in VLSI

The main goal of this article is to implement an effective Non-Blocking Benes switching Network. Benes Switching Network is designed with the uncomplicated switch modules & it’s have so many advantages, small latency, less traffic and it’s required number of switch modules. Clos and Benes networks are play a key role in the class of multistage interconnection network because of their extensibility and mortality. Benes network provides a low latency when compare with the other networks. 8x8 Benes non blocking switching network is designed and synthesized with the using of Xilinx tool 12.1.

Multi-stage Interconnection networks CLOS/BENES Parallel Routing Algorithms for circuit switching system

This article approaches the design of parallel routing Clos and Benes switching networks in Communication Technology. In communication, the transmission of data with less traffic and low latency are the biggest challenges. The conventional packet switching circuits takes the more power and high area to overcome this problem parallel routing algorithms are proposed. Clos and Benes networks are designed for the circuit switching systems where the switching configuration will be rearranged and it’s relatively low speed. Most of the existing parallel routing algorithms are not practical those are fail to interconnects the inputs with the matched outputs with less traffic. In this article, we designed Clos and Benes network. Clos and Benes networks are the Non-blocking switching Networks. Clos Switching network provides the better results like low area and less delay when compare with the Benes Switching Network. Clos and Benes non-blocking switching circuits are designed by Verilog HDL, Synthesized and simulated by XILINX 12.1 tool

The Performance on Slope Number of Hypercube, Normal Representation of Butterfly and Benes Networks

Many quality measures have been defined for graph drawings. In order to optimize these measures, slope number is considered to minimize the distinct edge slopes. The edges of the graphs are designed here as straight line segments. A number of distinct slopes required to draw the graph is called slope number. In this paper the slopenumber is discussed for known parallel architectures like hypercube, butterfly and benes networks. In addition to that the characterization of these networks is investigated and the results are observed for the defined problem.

Tight Bounds on 1-Harmonious Coloring of Certain Graphs

Graph coloring is one of the most studied problems in graph theory due to its important applications in task scheduling and pattern recognition. The main aim of the problem is to assign colors to the elements of a graph such as vertices and/or edges subject to certain constraints. The 1-harmonious coloring is a kind of vertex coloring such that the color pairs of end vertices of every edge are different only for adjacent edges and the optimal constraint that the least number of colors is to be used. In this paper, we investigate the graphs in which we attain the sharp bound on 1-harmonious coloring. Our investigation consists of a collection of basic graphs like a complete graph, wheel, star, tree, fan, and interconnection networks such as a mesh-derived network, generalized honeycomb network, complete multipartite graph, butterfly, and Benes networks. We also give a systematic and elegant way of coloring for these structures.