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...

Ausführliche Beschreibung

Bibliographische Detailangaben

Hauptverfasser:	Wagner, Stephan 1982- (VerfasserIn), Wang, Hua (VerfasserIn)
Format:	Elektronisch E-Book
Sprache:	English
Veröffentlicht:	Boca Raton ; London ; New York CRC Press [2019]
Schriftenreihe:	Discrete mathematics and its applications series
Online-Zugang:	TUM01
Zusammenfassung:	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
Beschreibung:	1 Online-Ressource
ISBN:	9780429833984