Irregularity in Graphs

Akbar Ali, Gary Chartrand, Ping Zhang (Autoren)

Buch | Softcover

X, 109 Seiten

2021 | 1st ed. 2021
Springer International Publishing (Verlag)
978-3-030-67992-7 (ISBN)

Artikel merken

Die Theorie der regularen Graphen (The Theory of Regular Graphs), written by the Danish Mathematician Julius Petersen in 1891, is often considered the first strictly theoretical paper dealing with graphs. In the 130 years since then, regular graphs have been a common and popular area of study. While regular graphs are typically considered to be graphs whose vertices all have the same degree, a more general interpretation is that of graphs possessing some common characteristic throughout their structure.
During the past several decades, however, there has been some increased interest in investigating graphs possessing a property that is, in a sense, opposite to regularity. It is this topic with which this book deals, giving rise to a study of what might be called irregularity in graphs. Here, various irregularity concepts dealing with several topics in graph theory are described, such as degrees of vertices, graph labelings, weightings, colorings, graph structures, Eulerian and Hamiltonian properties, graph decompositions, and Ramsey-type problems.

1. Introduction.- 2. Locally Irregular Graphs.- 3. F-Irregular Graphs.- 4. Irregularity Strength.- 5. Rainbow Mean Index.- 6. Royal Colorings.- 7. Traversable Irregularity.- 8. Ascending Subgraph Decompositions.- Index.

"The book is relatively short (109 pages) but rich in topics. ... The book can serve as a reference source ... or as a textbook for an undergraduate exploratory graph theory course or seminar. It contains a wealth of easy to understand open problems that can inspire enthusiastic students to turn their focus to further study of graph theory." (Dalibor Froncek, zbMATH 1472.05001, 2021)

“The book is relatively short (109 pages) but rich in topics. … The book can serve as a reference source … or as a textbook for an undergraduate exploratory graph theory course or seminar. It contains a wealth of easy to understand open problems that can inspire enthusiastic students to turn their focus to further study of graph theory.” (Dalibor Fronček, zbMATH 1472.05001, 2021)

Erscheinungsdatum	22.05.2021
Reihe/Serie	SpringerBriefs in Mathematics
Zusatzinfo	X, 109 p. 62 illus.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Gewicht	195 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Graphentheorie
Schlagworte	edge coloring • Eulerian and Hamiltonian irregularity • highly irregular graphs • irregular coloring • Irregularity • irregular weightings • labelings • link-irregular graphs • Rainbow coloring • Ramsey-type problems • rregular decomposition
ISBN-10	3-030-67992-6 / 3030679926
ISBN-13	978-3-030-67992-7 / 9783030679927
Zustand	Neuware