scholarly journals Sun Toughness Conditions for P 2 and P 3 Factor Uniform and Factor Critical Avoidable Graphs

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Shu Gong ◽  
Haci Mehmet Baskonus ◽  
Wei Gao
Keyword(s):  
Graph Theory ◽  
Computer Networks ◽  
The Sun ◽  
Graph Structure ◽  
Network Graph ◽  
The Given ◽  
Path Factor

The security of a network is closely related to the structure of the network graph. The denser the network graph structure is, the better it can resist attacks. Toughness and isolated toughness are used to characterize the vulnerable programs of the network which have been paid attention from mathematics and computer scholars. On this basis, considering the particularity of the sun component structures, sun toughness was introduced in mathematics and applied to computer networks. From the perspective of modern graph theory, this paper presents the sun toughness conditions of the path factor uniform graph and the path factor critical avoidable graph in P ≥ 2 -factor and P ≥ 3 -factor settings. Furthermore, examples show that the given boundaries are sharp.

Pattern Recognition in Histo-Pathology: Basic Considerations

1982 ◽  
Vol 21 (01) ◽  
pp. 15-22 ◽  
Author(s):  
W. Schlegel ◽  
K. Kayser
Keyword(s):  
Pattern Recognition ◽  
Graph Theory ◽  
Normal Tissue ◽  
Diagnostic Procedures ◽  
Minimal Distance ◽  
Malignant Growth ◽  
Colon Tissue ◽  
First Results ◽  
Tissue Structures ◽  
The Given

A basic concept for the automatic diagnosis of histo-pathological specimen is presented. The algorithm is based on tissue structures of the original organ. Low power magnification was used to inspect the specimens. The form of the given tissue structures, e. g. diameter, distance, shape factor and number of neighbours, is measured. Graph theory is applied by using the center of structures as vertices and the shortest connection of neighbours as edges. The algorithm leads to two independent sets of parameters which can be used for diagnostic procedures. First results with colon tissue show significant differences between normal tissue, benign and malignant growth. Polyps form glands that are twice as wide as normal and carcinomatous tissue. Carcinomas can be separated by the minimal distance of the glands formed. First results of pattern recognition using graph theory are discussed.

An Algorithm for the Enumeration of Serial and/or Parallel Combinations of Kinematic Building Blocks

2004 ◽  
Author(s):  
Hong-Sen Yan ◽  
Feng-Ming Ou ◽  
Ming-Feng Tang
Keyword(s):  
Graph Theory ◽  
Building Blocks ◽  
Power Source ◽  
Cam Follower ◽  
Tree Representations ◽  
The Given

An algorithm is presented, based on graph theory, for enumerating all feasible serial and/or parallel combined mechanisms from the given rotary or translational power source and specific kinematic building blocks. Through the labeled out-tree representations for the configurations of combined mechanisms, the enumeration procedure is developed by adapting the algorithm for the enumeration of trees. A rotary power source and four kinematic building blocks: a crank-rocker linkage, a rack-pinion, a double-slider mechanism, and a cam-follower mechanism, are chosen as the combination to illustrate the algorithm. And, two examples are provided to validate the algorithm.

scholarly journals Graph Theoretic Techniques in the Analysis of Uniquely Localizable Sensor Networks

2009 ◽  
pp. 146-173 ◽  
Author(s):  
Bill Jackson ◽  
Tibor Jordán
Keyword(s):  
Graph Theory ◽  
Sensor Networks ◽  
Optimization Problems ◽  
Partial Information ◽  
Two Dimensions ◽  
Localization Problem ◽  
Graph Theoretic ◽  
Network Localization ◽  
Exact Location ◽  
The Given

In the network localization problem the goal is to determine the location of all nodes by using only partial information on the pairwise distances (and by computing the exact location of some nodes, called anchors). The network is said to be uniquely localizable if there is a unique set of locations consistent with the given data. Recent results from graph theory and combinatorial rigidity made it possible to characterize uniquely localizable networks in two dimensions. Based on these developments, extensions, related optimization problems, algorithms, and constructions also became tractable. This chapter gives a detailed survey of these new results from the graph theorist’s viewpoint.

scholarly journals Cryptosystem using double vertex graph

2020 ◽  
Vol 13 (44) ◽  
pp. 4483-4489
Author(s):  
C Beaula ◽  
Keyword(s):  
Graph Theory ◽  
Secure Communication ◽  
System Method ◽  
Encryption And Decryption ◽  
Vertex Graph ◽  
Private And Public ◽  
Almost All ◽  
Encryption Method ◽  
The Given ◽  
Edge Labeling

Background/Objective: The Coronavirus Covid-19 has affected almost all the countries and millions of people got infected and more deaths have been reported everywhere. The uncertainty and fear created by the pandemic can be used by hackers to steal the data from both private and public systems. Hence, there is an urgent need to improve the security of the systems. This can be done only by building a strong cryptosystem. So many researchers started embedding different topics of mathematics like algebra, number theory, and so on in cryptography to keep the system, safe and secure. In this study, a cryptosystem using graph theory has been attempted, to strengthen the security of the system. Method: A new graph is constructed from the given graph, known as a double vertex graph. The edge labeling of this double vertex graph is used in encryption and decryption. Findings: A new cryptosystem using the amalgamation of the path, its double vertex graph and edge labeling has been proposed. From the double vertex graph of a path, we have given a method to find the original path. To hack such an encrypted key, the knowledge of graph theory is important, which makes the system stronger. Applications:The one-word encryption method will be useful in every security system that needs a password for secure communication or storage or authentication. Keywords: Double vertex graphs; path; adjacency matrix; encryption; cryptography

River System Connectivity Analysis of Wuxi’s Central Urban Area Based on Graph Theory

2012 ◽  
Vol 212-213 ◽  
pp. 543-548 ◽  
Author(s):  
Liu Yan Wang ◽  
You Peng Xu ◽  
Ming Jing Yu
Keyword(s):  
Graph Theory ◽  
Urban Area ◽  
Water Environment ◽  
River System ◽  
Yangtze River Delta ◽  
River Network ◽  
Structure Stability ◽  
Network Graph ◽  
Stream Structure ◽  
Wuxi City

Wuxi City is located in the hinterland of Taihu Basin and an important city in Yangtze River Delta Region with a prosperous economy. In the process of urban development, the river system pattern changes a lot. It has an impact on water environment, water ecology and other fields. The central urban area of Wuxi City was selected as the study area. Based on the river system of three periods: 1960s, 1980s and 2009, the rivers were classified into three levels according to the width of channels. The length, acreage and stream structure parameters were calculated. Then from the view of Graph Theory, river system was expressed as network graph, and the vertices, edges and degree of vertices were analyzed. The results show that the changes of rivers of different levels and lakes are not completely the same, but still appear a decreasing trend in general. The river network density and water surface ratio become smaller. Also the complexity and structure stability of river network weaken. The conclusions that the river evolution tends to be trunk and single, the stream structure is simplified and the connectivity of rivers and lakes reduces are verified by the analysis based on Graph Theory as well.

scholarly journals The Fan–Raspaud conjecture: A randomized algorithmic approach and application to the pair assignment problem in cubic networks

2012 ◽  
Vol 22 (3) ◽  
pp. 765-778
Author(s):  
Piotr Formanowicz ◽  
Krzysztof Tanaś
Keyword(s):  
Graph Theory ◽  
Computer Networks ◽  
Assignment Problem ◽  
Perfect Matchings ◽  
Cubic Graphs ◽  
Cubic Graph ◽  
Algorithmic Approach ◽  
Edge Colorings ◽  
Mathematical Properties

Abstract It was conjectured by Fan and Raspaud (1994) that every bridgeless cubic graph contains three perfect matchings such that every edge belongs to at most two of them. We show a randomized algorithmic way of finding Fan–Raspaud colorings of a given cubic graph and, analyzing the computer results, we try to find and describe the Fan–Raspaud colorings for some selected classes of cubic graphs. The presented algorithms can then be applied to the pair assignment problem in cubic computer networks. Another possible application of the algorithms is that of being a tool for mathematicians working in the field of cubic graph theory, for discovering edge colorings with certain mathematical properties and formulating new conjectures related to the Fan–Raspaud conjecture.

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