Computational techniques and data structures of the sparse underdetermined systems with using graph theory

2016 ◽  
Author(s):  
L. A. Pilipchuk ◽  
A. S. Pilipchuk
Keyword(s):  
Graph Theory ◽  
Data Structures ◽  
Computational Techniques ◽  
Underdetermined Systems

scholarly journals Atomic-scale one-dimensional materials identified from graph theory

2021 ◽  
Author(s):  
Shunning Li ◽  
Zhefeng Chen ◽  
Zhi Wang ◽  
Mouyi Weng ◽  
Jianyuan Li ◽  
...  
Keyword(s):  
Graph Theory ◽  
Structural Information ◽  
Functional Materials ◽  
Atomic Scale ◽  
Computational Techniques ◽  
Electronic Band ◽  
One Dimensional ◽  
Atomic Chains ◽  
Future Data ◽  
Low Dimensional

Abstract The past decades have witnessed an exponential growth in the discovery of functional materials, benefited from our unprecedented capabilities in characterizing their structure, chemistry, and morphology with the aid of advanced imaging, spectroscopic and computational techniques. Among these materials, atomic-scale low-dimensional compounds, as represented by the two-dimensional (2D) atomic layers, one-dimensional (1D) atomic chains and zero-dimensional (0D) atomic clusters, have long captivated scientific interest due to their unique topological motifs and exceptional properties. Their tremendous potentials in various applications make it a pressing urgency to establish a complete database of their structural information, especially for the underexplored 1D species. Here we apply graph theory in combination with first-principles high-throughput calculations to identify atomic-scale 1D materials that can be conceptually isolated from their parent bulk crystals. In total, two hundred and fifty 1D atomic chains are shown to be potentially exfoliable. We demonstrate how the lone electron pairs on cations interact with the p-orbitals of anions and hence stabilize their edge sites. Data analysis of the 2D and 1D materials also reveals the dependence of electronic band gap on the cationic percolation network determined by graph theory. The library of 1D compounds systematically identified in this work will pave the way for the predictive discovery of material systems for quantum engineering, and can serve as a source of stimuli for future data-driven design and understanding of functional materials with reduced dimensionality.

Graph Applications to Data Structures

2012 ◽  
Vol 433-440 ◽  
pp. 3297-3301
Author(s):  
V. Manjula
Keyword(s):  
Graph Theory ◽  
Computer Science ◽  
Programming Languages ◽  
Data Structures ◽  
Applied Mathematics ◽  
Syntactic Analysis ◽  
Discrete Mathematics ◽  
Major Theme ◽  
Computer Algorithms ◽  
Mathematical Programs

This paper presents a topic on Graph theory and its application to data Structures which I consider basic and useful to students in APPLIED MATHEMATICS and ENGINEERING.This paper gives an elementary introduction of Graph theory and its application to data structures. Elements of Graph theory are indispensable in almost all computer Science areas .It can be used in Some areas such as syntactic analysis, fault detection, diagnosis in computers and minimal path problems. The computer representation and manipulation of graph are also discussed so that certain algorithms can be included .A major theme of this paper is to study Graph theory and its Application to data structures Furthermore I hope the students not only learn the course but also develop their analogy perceive, formulate and to solve mathematical programs Thus Graphs especially trees, binary trees are used widely in the representation of data structures this course one can develop mathematical maturity, ability to understand and create mathematical argumentsMethod of derivation is procedure given in the text books with necessary formulae and their application . Concepts and notations from discrete mathematics are useful in studying and describing objects and problems in branches of computer science, such as computer algorithms, programming languages.

scholarly journals Review on Chemical Graph Theory and Its Application in Computer-Assisted Structure Elucidation

2021 ◽  
Author(s):  
Mehmet Aziz Yirik ◽  
Kumsal Ecem Colpan ◽  
Saskia Schmidt ◽  
Maria Sorokina ◽  
Christoph Steinbeck
Keyword(s):  
Graph Theory ◽  
Data Structures ◽  
Computer Assisted ◽  
Structure Property ◽  
Chemical Graph ◽  
Chemical Structures ◽  
Chemical Graph Theory ◽  
Structure Activity ◽  
History Of ◽  
Computer Assisted Structure Elucidation

The chemical graph theory is a subfield of mathematical chemistry which applies classic graph theory to chemical entities and phenomena. Chemical graphs are main data structures to represent chemical structures in cheminformatics. Computable properties of graphs lay the foundation for (quantitative) structure activity and structure property predictions - a core discipline of cheminformatics. It has a historic relevance for natural sciences, such as chemistry, biochemistry and biology, and is in the heart of modern disciplines, such as cheminformatics and bioinformatics. This review first covers the history of chemical graph theory, then provides an overview of its various techniques and applications for CASE, and finally summarises modern tools using chemical graph theory for CASE.

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