| Description |
1 online resource |
| Contents |
Cover -- Half Title -- Title Page -- Copyright Page -- Contents -- Preface -- About the Authors -- Symbols -- 1. Decompositions of Graphs: An Introduction -- 1.1. The Early Developments of Concepts of Decompositions -- 1.2. Basic Terminologies -- 1.2.1. Digraphs -- 1.2.2. Block Designs -- I. Decompositions into Cyclic Graphs -- 2. Cycle Decompositions -- 2.1. Cm-Decompositions -- 2.1.1. Decomposition of Kn into m-Cycles and a Perfect Matching -- 2.2. Cycles of Varying Lengths -- 2.3. Hamilton Decompositions -- 2.4. Hajós' Conjecture -- 2.5. Open Problems -- 3. Digraph Decompositions |
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3.1. Hamilton Directed Graph Decompositions -- 3.2. Cycles of Varying Lengths -- 3.3. Bermond-Thomassen Conjecture -- 3.4. Lichiardopol's Conjecture -- 3.5. Kelly's Conjecture -- 3.6. Some Other Conjectures on Digraphs -- 3.7. Open Problems -- 4. K4 − e Decompositions -- 4.1. Block Design of Graphs -- 4.2. Spectrum of K4 − e Designs -- 4.3. Resolvable K4 − e Designs -- 4.4. Intersection Problem of K4 − e Designs -- 4.5. The K4 − e Designs of Graphs with Small Orders -- 4.5.1. Some Constructions on K4 − e Designs -- 4.6. Open Problems -- II. Decompositions into Acyclic Graphs |
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5. Tree Decompositions -- 5.1. Treewidth, Pathwidth, and Branchwidth -- 5.2. Some Other Methods -- 5.3. Barát-Thomassen Conjecture -- 5.4. Kotzig-Ringel-Rosa Conjecture -- 5.5. Ringel's Conjecture -- 5.6. Open Problems -- 6. Path Decompositions -- 6.1. Path Number of a Graph -- 6.1.1. Graphoidal Cover -- 6.2. Pk Decompositions -- 6.2.1. P3 Decompositions -- 6.2.2. P4 Decompositions -- 6.2.3. P5 Decompositions -- 6.3. Path Decompositions using Girth -- 6.4. Path Decompositions of Digraphs -- 6.5. Paths of Varying Lengths -- 6.6. Gallai's Conjecture -- 6.7. Open Problems -- 7. Star Decompositions |
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7.1. Sk Decompositions -- 7.2. Claw-Decompositions -- 7.3. Stars of Varying Lengths -- 7.4. Double Star Decompositions -- 7.5. Star Decompositions of Digraphs -- 7.6. Spectrum and Intersection Problems -- 7.7. Star Number of Graphs -- 7.8. Open Problems -- 8. Pendant Number of Graphs -- 8.1. Pendant Number -- 8.2. Properties of Pendant Number -- 8.3. Equipendant, Selfipendant and Extremal Pendant Graphs -- 8.4. Pendant Number of Line Graphs and Total Graphs -- 8.5. Pendant Number of Some Graph Products -- 8.5.1. Rooted Products -- 8.5.2. Corona Products -- 8.5.3. Cartesian Products |
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8.5.4. Direct Products -- 8.6. Path-Induced Signed Graphs -- 8.6.1. Path-Induced Signed Graphs -- 8.6.2. Balance in Path-Induced Signed Graphs -- 8.6.3. Pseudo-balancing of Path-Induced Signed Graphs -- 8.6.4. Clusterability in Path-Induced Signed Graphs -- 8.7. Marcin's Algorithm -- 8.8. Open Problems -- III. Decompositions into Multiple Graphs -- 9. Multiple Decompositions of Graphs -- 9.1. Decomposing Graphs into Pairs -- 9.1.1. {Pl, Sk} Decompositions -- 9.1.2. {Cl, Sk} Decompositions -- 9.1.3. {Pl, Ck} Decompositions -- 9.1.4. Complementing Pair (G, G) Decompositions |
| Summary |
The book Graph Theory and Decomposition covers major areas of the decomposition of graphs. It is a three-part reference book with nine chapters that is aimed at enthusiasts as well as research scholars. It comprehends historical evolution and basic terminologies, and it deliberates on decompositions into cyclic graphs, such as cycle, digraph, and K4-e decompositions. In addition to determining the pendant number of graphs, it has a discourse on decomposing a graph into acyclic graphs like general tree, path, and star decompositions. It summarises another recently developed decomposition technique, which decomposes the given graph into multiple types of subgraphs. Major conjectures on graph decompositions are elaborately discussed. It alludes to a comprehensive bibliography that includes over 500 monographs and journal articles. It includes more than 500 theorems, around 100 definitions, 56 conjectures, 40 open problems, and an algorithm. The index section facilitates easy access to definitions, major conjectures, and named theorems. Thus, the book Graph Theory and Decomposition will be a great asset, we hope, in the field of decompositions of graphs and will serve as a reference book for all who are passionate about graph theory |
| Notes |
Jomon Kottarathil (0000-0003-4787-6029) St. Joseph's College, Moolamattom jomoncmi@gmail.com Jomon Kottarathil (Jomon K Sebastian) secured his doctoral degree from Manonmaniam Sundaranar University, Tamil Nadu, India, on 'Decompositions of Graphs'. He currently serves as Head of the Department of Data Science and is an Assistant Professor of Mathematics at St. Joseph's College, Moolamattom, Kerala, India. He also serves as a member of panels of referees for many international research journals and is a life member of professional societies. He has authored around 20 research articles in graph theory and more than 20 literary articles in the vernacular language of Malayalam. He attended around 35 conferences and presented papers. He holds postgraduate degrees in mathematics and education and has over 15 years of teaching experience and about 10 years of research experience. Sudev Naduvath (0000-0001-9692-4053) CHRIST(Deemed to be University), Bengaluru sudev.nk@christuniversity.in Sudev Naduvath secured his doctoral degree from Kannur University, Kerala, India, on 'Set- Valuations of Discrete Structures and Their Applications'. He currently serves as Associate Professor of Mathematics at CHRIST (Deemed to be University), Bengaluru, India. He has authored 127 researcharticles, 3 books, and 4 book chapters. He is a member of the panels of referees for 52 journals and a member of the board of editors for 11 journals. He has membership in 13 professional societies. He has about 20 years of teaching experience 10 years of research experience, and he is currently supervising seven doctoral students. Joseph Varghese Kureethara(0000-0001-5030-3948) CHRIST (Deemed to be University), Bengaluru frjoseph@christuniversity.in Joseph Varghese Kureethara secured his doctoral degree from Manonmaniam Sundaranar University, Tirunelveli, India, on 'Observations in Continuous Monotonic Decomposition of Connected Graphs: Special Cases in Complete Tripartite Graphs and Other Related Topics'. He currently serves as a Professor of Mathematics and is heading the Centre for Research at CHRIST(Deemed to be University), Bengaluru, India. He has over eighteen years of experience in teaching and research and has published 148 articles, of which 77 are Scopus-indexed, and 38 are in the Web of Science core collection. His areas of interest are Graph Theory, Number Theory, Fuzzy Optimisation, and Education. He has supervised six PhDs, 12 MPhils, and is supervising eight PhDs |
| Subject |
Graph theory.
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Decomposition (Mathematics)
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MATHEMATICS / Discrete Mathematics
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MATHEMATICS / Applied
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| Genre/Form |
Electronic books
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| Form |
Electronic book
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| Author |
Naduvath, Sudev
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Kureethara, Joseph Varghese.
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| ISBN |
9781040018736 |
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1040018734 |
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9781003391678 |
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1003391672 |
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9781040018767 |
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1040018769 |
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