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Handbook of Research on Advanced Applications of Graph Theory in Modern Society最新文献

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A Novel Weighted First Zagreb Index of Graph 图的一种新的加权第一Zagreb指数
Handbook of Research on Advanced Applications of Graph Theory in Modern Society Pub Date : 1900-01-01 DOI: 10.4018/978-1-5225-9380-5.CH004
J. Buragohain, A. Bharali
{"title":"A Novel Weighted First Zagreb Index of Graph","authors":"J. Buragohain, A. Bharali","doi":"10.4018/978-1-5225-9380-5.CH004","DOIUrl":"https://doi.org/10.4018/978-1-5225-9380-5.CH004","url":null,"abstract":"The Zagreb indices are the oldest among all degree-based topological indices. For a connected graph G, the first Zagreb index M1(G) is the sum of the term dG(u)+dG(v) corresponding to each edge uv in G, that is, M1 , where dG(u) is degree of the vertex u in G. In this chapter, the authors propose a weighted first Zagreb index and calculate its values for some standard graphs. Also, the authors study its correlations with various physico-chemical properties of octane isomers. It is found that this novel index has strong correlation with acentric factor and entropy of octane isomers as compared to other existing topological indices.","PeriodicalId":163154,"journal":{"name":"Handbook of Research on Advanced Applications of Graph Theory in Modern Society","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125412925","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Graph Theory 图论
Handbook of Research on Advanced Applications of Graph Theory in Modern Society Pub Date : 1900-01-01 DOI: 10.4018/978-1-5225-9380-5.CH014
R. Seethalakshmi
{"title":"Graph Theory","authors":"R. Seethalakshmi","doi":"10.4018/978-1-5225-9380-5.CH014","DOIUrl":"https://doi.org/10.4018/978-1-5225-9380-5.CH014","url":null,"abstract":"Mathematics acts an important and essential need in different fields. One of the significant roles in mathematics is played by graph theory that is used in structural models and innovative methods, models in various disciplines for better strategic decisions. In mathematics, graph theory is the study through graphs by which the structural relationship studied with a pair wise relationship between different objects. The different types of network theory or models or model of the network are called graphs. These graphs do not form a part of analytical geometry, but they are called graph theory, which is points connected by lines. The various concepts of graph theory have varied applications in diverse fields. The chapter will deal with graph theory and its application in various financial market decisions. The topological properties of the network of stocks will provide a deeper understanding and a good conclusion to the market structure and connectivity. The chapter is very useful for academicians, market researchers, financial analysts, and economists.","PeriodicalId":163154,"journal":{"name":"Handbook of Research on Advanced Applications of Graph Theory in Modern Society","volume":"61 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116523654","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Applying Graph Theory to Detect Cases of Money Laundering and Terrorism Financing 图论在洗钱与恐怖融资案件侦查中的应用
Handbook of Research on Advanced Applications of Graph Theory in Modern Society Pub Date : 1900-01-01 DOI: 10.4018/978-1-5225-9380-5.CH012
N. Miloslavskaya, A. Nikiforov, Kirill V. Plaksiy, A. Tolstoy
{"title":"Applying Graph Theory to Detect Cases of Money Laundering and Terrorism Financing","authors":"N. Miloslavskaya, A. Nikiforov, Kirill V. Plaksiy, A. Tolstoy","doi":"10.4018/978-1-5225-9380-5.CH012","DOIUrl":"https://doi.org/10.4018/978-1-5225-9380-5.CH012","url":null,"abstract":"A technique to automate the generation of criminal cases for money laundering and financing of terrorism (ML/FT) based on typologies is proposed. That will help an automated system from making a decision about the exact coincidence when comparing the case objects and their links with those in the typologies. Several types of subgraph changes (mutations) are examined. The main goal to apply these mutations is to consider other possible ML/FT variants that do not correspond explicitly to the typologies but have a similar scenario. Visualization methods like the graph theory are used to order perception of data and to reduce its volumes. This work also uses the foundations of information and financial security. The research demonstrates possibilities of applying the graph theory and big data tools in investigating information security incidents. A program has been written to verify the technique proposed. It was tested on case graphs built on the typologies under consideration.","PeriodicalId":163154,"journal":{"name":"Handbook of Research on Advanced Applications of Graph Theory in Modern Society","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127582604","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Graph Indices 图指数
Handbook of Research on Advanced Applications of Graph Theory in Modern Society Pub Date : 1900-01-01 DOI: 10.4018/978-1-5225-9380-5.ch003
V. Kulli
{"title":"Graph Indices","authors":"V. Kulli","doi":"10.4018/978-1-5225-9380-5.ch003","DOIUrl":"https://doi.org/10.4018/978-1-5225-9380-5.ch003","url":null,"abstract":"A molecular graph is a finite simple graph representing the carbon-atom skeleton of an organic molecule of a hydrocarbon. Studying molecular graphs is a constant focus in chemical graph theory: an effort to better understand molecular structure. Many types of graph indices such as degree-based graph indices, distance-based graph indices, and counting-related graph indices have been explored recently. Among degree-based graph indices, Zagreb indices are the oldest and studied well. In the last few years, many new graph indices were proposed. The present survey of these graph indices outlines their mathematical properties and also provides an exhaustive bibliography.","PeriodicalId":163154,"journal":{"name":"Handbook of Research on Advanced Applications of Graph Theory in Modern Society","volume":"47 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133784348","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 18
Energy of Graphs 图的能量
Handbook of Research on Advanced Applications of Graph Theory in Modern Society Pub Date : 1900-01-01 DOI: 10.4018/978-1-5225-9380-5.CH011
H. Ramane
{"title":"Energy of Graphs","authors":"H. Ramane","doi":"10.4018/978-1-5225-9380-5.CH011","DOIUrl":"https://doi.org/10.4018/978-1-5225-9380-5.CH011","url":null,"abstract":"The energy of a graph G is defined as the sum of the absolute values of the eigenvalues of its adjacency matrix. The graph energy has close correlation with the total pi-electron energy of molecules calculated with Huckel molecular orbital method in chemistry. A graph whose energy is greater than the energy of complete graph of same order is called hyperenergetic graph. A non-complete graph having energy equal to the energy of complete graph is called borderenergetic graph. Two non-cospectral graphs are said to be equienergetic graphs if they have same energy. In this chapter, the results on graph energy are reported. Various bounds for graph energy and its characterization are summarized. Construction of hyperenergetic, borderenergetic, and equienergetic graphs are reported.","PeriodicalId":163154,"journal":{"name":"Handbook of Research on Advanced Applications of Graph Theory in Modern Society","volume":"102 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116295292","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 4
Sumset Valuations of Graphs and Their Applications 图的Sumset赋值及其应用
Handbook of Research on Advanced Applications of Graph Theory in Modern Society Pub Date : 1900-01-01 DOI: 10.4018/978-1-5225-9380-5.ch009
S. Naduvath, Germina K. Augusthy, J. Kok
{"title":"Sumset Valuations of Graphs and Their Applications","authors":"S. Naduvath, Germina K. Augusthy, J. Kok","doi":"10.4018/978-1-5225-9380-5.ch009","DOIUrl":"https://doi.org/10.4018/978-1-5225-9380-5.ch009","url":null,"abstract":"Graph labelling is an assignment of labels to the vertices and/or edges of a graph with respect to certain restrictions and in accordance with certain predefined rules. The sumset of two non-empty sets A and B, denoted by A+B, is defined by A+B={a=b: ainA, binB}. Let X be a non-empty subset of the set Z and sP(X) be its power set. An textit{sumset labelling} of a given graph G is an injective set-valued function f: V(G)tosP_0(X), which induces a function f+: E(G)tosP_0(X) defined by f+(uv)=f(u)+f(v), where f(u)+f(v) is the sumset of the set-labels of the vertices u and v. This chapter discusses different types of sumset labeling of graphs and their structural characterizations. The properties and characterizations of certain hypergraphs and signed graphs, which are induced by the sumset-labeling of given graphs, are also done in this chapter.","PeriodicalId":163154,"journal":{"name":"Handbook of Research on Advanced Applications of Graph Theory in Modern Society","volume":"114 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116485486","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
Fuzzy Graphs and Fuzzy Hypergraphs 模糊图和模糊超图
Handbook of Research on Advanced Applications of Graph Theory in Modern Society Pub Date : 1900-01-01 DOI: 10.4018/978-1-5225-9380-5.CH019
M. Voskoglou, Tarasankar Pramanik
{"title":"Fuzzy Graphs and Fuzzy Hypergraphs","authors":"M. Voskoglou, Tarasankar Pramanik","doi":"10.4018/978-1-5225-9380-5.CH019","DOIUrl":"https://doi.org/10.4018/978-1-5225-9380-5.CH019","url":null,"abstract":"Relationship is the core building block of a network, and today's world advances through the complex networks. Graph theory deals with such problems more efficiently. But whenever vagueness or imprecision arises in such relationships, fuzzy graph theory helps. However, fuzzy hypergraphs are more advanced generalization of fuzzy graphs. Whenever there is a need to define multiary relationship rather than binary relationship, one can use fuzzy hypergraphs. In this chapter, interval-valued fuzzy hypergraph is discussed which is a generalization of fuzzy hypergraph. Several approaches to find shortest path between two given nodes in an interval-valued fuzzy graphs is described here. Many researchers have focused on fuzzy shortest path problem in a network due to its importance to many applications such as communications, routing, transportation, etc.","PeriodicalId":163154,"journal":{"name":"Handbook of Research on Advanced Applications of Graph Theory in Modern Society","volume":"41 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124380684","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
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