A Study of Regular and Irregular Neutrosophic Graphs with Real Life Applications

Fuzzy graph theory is a useful and well-known tool to model and solve many real-life optimization problems. Since real-life problems are often uncertain due to inconsistent and indeterminate information, it is very hard for an expert to model those problems using a fuzzy graph. A neutrosophic graph can deal with the uncertainty associated with the inconsistent and indeterminate information of any real-world problem, where fuzzy graphs may fail to reveal satisfactory results. The concepts of the regularity and degree of a node play a significant role in both the theory and application of graph theory in the neutrosophic environment. In this work, we describe the utility of the regular neutrosophic graph and bipartite neutrosophic graph to model an assignment problem, a road transport network, and a social network. For this purpose, we introduce the definitions of the regular neutrosophic graph, star neutrosophic graph, regular complete neutrosophic graph, complete bipartite neutrosophic graph, and regular strong neutrosophic graph. We define the d m - and t d m -degrees of a node in a regular neutrosophic graph. Depending on the degree of the node, this paper classifies the regularity of a neutrosophic graph into three types, namely d m -regular, t d m -regular, and m-highly irregular neutrosophic graphs. We present some theorems and properties of those regular neutrosophic graphs. The concept of an m-highly irregular neutrosophic graph on cycle and path graphs is also investigated in this paper. The definition of busy and free nodes in a regular neutrosophic graph is presented here. We introduce the idea of the &mu -complement and h-morphism of a regular neutrosophic graph. Some properties of complement and isomorphic regular neutrosophic graphs are presented here. Document type: Articl

Speeding Up VLSI Layout Verification Using Fuzzy Attributed Graphs Approach

Technical and economic factors have caused the field of physical design automation to receive increasing attention and commercialization. The steady down-scaling of complementary metal oxide semiconductor (CMOS) device dimensions has been the main stimulus to the growth of microelectronics and computer-aided very large scale integration (VLSI) design. The more an Integrated Circuit (IC) is scaled, the higher its packing density becomes. For example, in 2006 Intel\u27s 65-nm process technology for high performance microprocessor has a reduced gate length of 35 nanometers. In their 70-Mbit SRAM chip, there are up to 0.5 billion transistors in a 110 mm2 chip size with 3.4 GHz clock speed. New technology generations come out every two years and provide an approximate 0.7 times transistor size reduction as predicted by Moore\u27s Law. For the ultimate scaled MOSFET beyond 2015 or so, the transistor gate length is projected to be 10 nm and below. The continually increasing size of chips, measured in either area or number of transistors, and the wasted investment involving fabricating and testing faulty circuits, make layout analysis an important part of physical design automation. Layout-versus-schematic (LVS) is one of three kinds of layout analysis tools. Subcircuit extraction is the key problem to be solved in LVS. In LVS, two factors are important. One is run time, the other is identification correctness. This has created a need for computational intelligence. Fuzzy attributed graph is not only widely used in the fields of image understanding and pattern recognition, it is also useful to the fuzzy graph matching problem. Since the subcircuit extraction problem is a special case of a general-interest problem known as subgraph isomorphism, fuzzy attributed graphs are first effectively applied to the subgraph isomorphism problem. Then we provide an efficient fuzzy attributed graph algorithm based on the solution to subgraph isomorphism for the subcircuit extractio- n problem. Similarity measurement makes a significant contribution to evaluate the equivalence of two circuit graphs. To evaluate its performance, we compare fuzzy attributed graph approach with the commercial software called SubGemini, and two of the fastest approaches called DECIDE and SubHDP. We are able to achieve up to 12 times faster performance than alternatives, without loss of accurac

Algebraic Structures of Neutrosophic Triplets, Neutrosophic Duplets, or Neutrosophic Multisets

Neutrosophy (1995) is a new branch of philosophy that studies triads of the form (, , ), where is an entity {i.e. element, concept, idea, theory, logical proposition, etc.}, is the opposite of , while is the neutral (or indeterminate) between them, i.e., neither nor .Based on neutrosophy, the neutrosophic triplets were founded, which have a similar form (x, neut(x), anti(x)), that satisfy several axioms, for each element x in a given set.This collective book presents original research papers by many neutrosophic researchers from around the world, that report on the state-of-the-art and recent advancements of neutrosophic triplets, neutrosophic duplets, neutrosophic multisets and their algebraic structures – that have been defined recently in 2016 but have gained interest from world researchers. Connections between classical algebraic structures and neutrosophic triplet / duplet / multiset structures are also studied. And numerous neutrosophic applications in various fields, such as: multi-criteria decision making, image segmentation, medical diagnosis, fault diagnosis, clustering data, neutrosophic probability, human resource management, strategic planning, forecasting model, multi-granulation, supplier selection problems, typhoon disaster evaluation, skin lesson detection, mining algorithm for big data analysis, etc