A New Approach To Design Reliable General Sensor Network on the Basis of Graph Theory

This study presents a new approach to determine the controllability and observability of a large scale nonlinear dynamic thermal system using graph-theory. The novelty of this method is in adapting graph theory for nonlinear class and establishing a graphic condition that describes the necessary and sufficient terms for a nonlinear class system to be controllable and observable, which equivalents to the analytical method of Lie algebra rank condition. The directed graph (digraph) is utilized to model the system, and the rule of its adaptation in nonlinear class is defined. Subsequently, necessary and sufficient terms to achieve controllability and observability condition are investigated through the structural property of a digraph called connectability. It will be shown that the connectability condition between input and states, as well as output and states of a nonlinear system are equivalent to Lie-algebra rank condition (LARC). This approach has been proven to be easier from a computational point of view and is thus found to be useful when dealing with a large system.

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Applications of Fuzzy Graph Theory Portrayed in Various Fields

10.21203/rs.3.rs-298268/v1 ◽

2021 ◽

Author(s):

Abdul Muneera ◽

T. Nageswara Rao ◽

R. V. N. Srinivasa ◽

J. Venkateswara Rao

Keyword(s):

Graph Theory ◽

Wireless Sensor Network ◽

Sensor Network ◽

Material Science ◽

Natural Sciences ◽

Wireless Sensor ◽

Fuzzy Graph ◽

Ecological Conditions ◽

Fuzzy Graphs ◽

Remote System

Abstract The intend of the paper is to grant the centrality of fuzzy graph (f-graph) hypothetical ideas and the uses of dominations in fuzzy graphs to different genuine circumstances in the territories of science and designing. It is seen an eminent development because of various applications in PC and correspondence, biomedical, atomic material science and science, interpersonal organizations, natural sciences and in different various regions. Interpersonal organizations are the zones where countless individuals are associated. A wireless sensor Network (WSN) remote system which comprises of spatially circulated independent sensors to screen the physical or ecological conditions, for example, pressure, temperature, sound and so forth and to communicate their data through the remote system to a fundamental area. This paper gives an audit of the employments of Fuzzy Graph theory in different sorts of fields.

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A New Technique to Solve the Instant Insanity Problem

JOURNAL OF ADVANCES IN MATHEMATICS ◽

10.24297/jam.v11i10.805 ◽

2016 ◽

Vol 11 (10) ◽

pp. 5766-5773

Author(s):

Salar Y Alsardary ◽

Hwee Jung Kim ◽

Julie George

Keyword(s):

Graph Theory ◽

Programming Language ◽

New Technique ◽

New Approach ◽

A New Technique

Instant Insanity [1] consists of four cubes, each of whose six faces are colored with one of the four colors: red, blue, white, and green. The object is to stack the cubes in such a way that each of the four colors appears on each side of the resulting column. See figure 1 below[2]. Traditionally, this could be solved using graph theory.However, in this article, we introduce a new technique to solve the problem without using graph theory. We also used a Perl programming language to implement the new approach for the Instant Insanity.

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