Keywords:
Graph theory.
;
Electronic books.
Description / Table of Contents:
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. The book covers some of the most commonly used mathematical approaches in the subject.
Type of Medium:
Online Resource
Pages:
1 online resource (271 pages)
Edition:
1st ed.
ISBN:
9780429833984
Series Statement:
Discrete Mathematics and Its Applications Series
URL:
https://ebookcentral.proquest.com/lib/geomar/detail.action?docID=5514734
DDC:
540.1/5115
Language:
English
Note:
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 -- 2.3.5 Sum of eccentricities -- 2.4 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 -- Chapter 3 Vertex degrees and the Randic ´index -- 3.1 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.
,
3.5.2 Structural properties of the optimal graphs -- 3.5.3 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 ´index -- 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 -- 4.7 Independence polynomial and matching polynomial -- Chapter 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.
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