Graph Theory and Decomposition

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.

1. Decompositions of Graphs: An introduction. 2. Cycle Decompositions 3. Digraph Decompositions 4. K4-e Decompositions 5. Tree Decompositions 6. Path Decompositions 7. Star Decompositions 8. Pendant Number of Graphs 9. Multiple Decompositions of Graphs 10. Bibliography 11. Index

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 Decom