| Description |
1 online resource (271 pages) |
| Series |
Discrete Mathematics and Its Applications Ser |
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Discrete Mathematics and Its Applications Ser
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| Contents |
Cover; Half Title; Series Editors; Title; Copyrights; Contents; Preface; Chapter 1 Preliminaries; 1.1 Basic graph notations; 1.2 Special types of graphs; 1.3 Trees; 1.4 Degrees in graphs; 1.5 Distance in graphs; 1.6 Independent sets and matchings; 1.7 Topological indices; Chapter 2 Distance in graphs and the Wiener index; 2.1 An overview; 2.2 Properties related to distances; 2.3 Extremal problems in general graphs and trees; 2.3.1 The Wiener index; 2.3.2 The distances between leaves; 2.3.3 Distance between internal vertices; 2.3.4 Distance between internal vertices and leaves |
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2.3.5 Sum of eccentricities2.4 The Wiener index of trees with a given degree sequence; 2.5 The Wiener index of trees with a given segment sequence . .; 2.5.1 The minimum Wiener index in trees with a given seg-ment sequence; 2.5.2 The maximum Wiener index in trees with a given seg-ment sequence; 2.5.3 Further characterization of extremal quasi-caterpillars; 2.5.4 Trees with a given number of segments; 2.6 General approaches; 2.6.1 Caterpillars; 2.6.2 Greedy trees; 2.6.3 Comparing greedy trees of different degree sequences and applications; 2.7 The inverse problem |
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Chapter 3 Vertex degrees and the Randic índex3.1 Introduction; 3.2 Degree-based indices in trees with a given degree sequence .; 3.2.1 Greedy trees; 3.2.2 Alternating greedy trees; 3.3 Comparison between greedy trees and applications; 3.3.1 Between greedy trees; 3.3.2 Applications to extremal trees; 3.3.3 Application to specific indices; 3.4 The Zagreb indices; 3.4.1 Graphs with M1 = M2; 3.4.2 Maximum M2(·) −M1(·) in trees; 3.4.3 Maximum M1(·) −M2(·) in trees; 3.4.4 Further analysis of the behavior of M1() M2(); 3.5 More on the ABC index; 3.5.1 Defining the optimal graph |
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3.5.2 Structural properties of the optimal graphs3.5.3 Proof of Theorem 3.5.1; 3.5.4 Acyclic, unicyclic, and bicyclic optimal graphs; 3.6 Graphs with a given matching number; 3.6.1 Generalized Randic índex; 3.6.2 Zagreb indices based on edge degrees; 3.6.3 The Atom-bond connectivity index; Chapter 4 Independent sets: Merrifield-Simmons index and Hosoya in- dex; 4.1 History and terminologies; 4.2 Merrifield-Simmons index and Hosoya index: elementary prop-erties; 4.3 Extremal problems in general graphs and trees; 4.4 Graph transformations; 4.5 Trees with fixed parameters; 4.6 Tree-like graphs |
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4.7 Independence polynomial and matching polynomialChapter 5 Graph spectra and the graph energy; 5.1 Matrices associated with graphs; 5.2 Graph spectra and characteristic polynomials; 5.3 The graph energy: elementary properties; 5.4 Bounds for the graph energy; 5.5 Extremal problems in trees; 5.6 Extremal problems in tree-like graphs; 5.7 Energy-like invariants; 5.7.1 Matching energy; 5.7.2 Laplacian energy; 5.7.3 Incidence energy and Laplacian-energy-like invariant .; 5.8 Other invariants based on graph spectra; 5.8.1 Spectral radius of a graph; 5.8.2 Estrada index; Bibliography; Index |
| Summary |
Introduction to Chemical Graph Theory is a concise introduction to the main topics and techniques in chemical graph theory, specifically the theory of topological indices. These include distance-based, degree-based, and counting-based indices. The book covers some of the most commonly used mathematical approaches in the subject. It is also written with the knowledge that chemical graph theory has many connections to different branches of graph theory (such as extremal graph theory, spectral graph theory) The authors wrote the book in an appealing way that attracts people to chemical graph theory. In doing so, the book is an excellent playground and general reference text on the subject, especially for young mathematicians with a special interest in graph theory. Key Features: A concise introduction to topological indices of graph theory Appealing to specialists and non-specialists alike Provides many techniques from current research About the Authors: Stephan Wagner grew up in Graz (Austria), where he also received his PhD from Graz University of Technology in 2006. Shortly afterwards, he moved to South Africa, where he started his career at Stellenbosch University as a lecturer in January 2007. His research interests lie mostly in combinatorics and related areas, including connections to other scientific fields such as physics, chemistry and computer science. Hua Wang received his PhD from University of South Carolina in 2005. He held a Visiting Research Assistant Professor position at University of Florida before joining Georgia Southern University in 2008. His research interests include combinatorics and graph theory, elementary number theory, and related problems |
| Notes |
Print version record |
| Subject |
Chemistry -- Mathematics.
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Graph theory.
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MATHEMATICS -- Combinatorics.
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SCIENCE -- Chemistry -- Physical & Theoretical.
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Chemistry.
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Graph energy.
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Graph Theory.
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Indices.
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Molecular.
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Chemistry -- Mathematics
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Graph theory
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| Form |
Electronic book
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| Author |
Wang, Hua
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| ISBN |
9780429833984 |
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0429833989 |
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0429833997 |
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9780429833991 |
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0429450532 |
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9780429450532 |
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