Graph theory, and graph labeling in particular, are fast-growing research areas in mathematics. New results are constantly being discovered and published at a rapidly increasing rate due to the enormous number of open problems and conjectures in the field. This book deals mainly with the super edge-antimagic branch of graph labeling. It is written for specialists, but could be read also by postgraduate or undergraduate students with high school knowledge of mathematics and a vibrant interest in problem-solving.
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5.0 out of 5 stars
For serious worker and puzzle solver,
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This review is from: Super Edge-Antimagic Graphs: A Wealth of Problems and Some Solutions (Paperback)
The real strength of this book is in the sub-heading "A Wealth of Problems and Some Solutions". To the serious researcher this indicates many open problems and conjectures through which they can work but it is also inviting to the interested amateur. As any reader of this volume will notice, many of the problems in graph labeling are easy to describe and understand. While this does not imply that they are easy to solve, it is encouraging to interested readers to be able to go straight to "the coalface".
Graphs are just collections of points connected by lines. Labelled graphs have numbers associated with the points, edges or perhaps both. Edge antimagic graphs have their numbers distributed so that the 2 vertex labels on each edge sum to a different total for each edge (if the edges are also labelled the sum is over the three labels for each edge). To make it harder, the label numbers are not just random, they start from 1 and continue, without gaps, for as many as you need. The term "super" just means that you label the vertices (points) first - using the lowest numbers, before labelling the edges. For individual graphs the problems are akin to puzzles in the Sunday papers but the real challenge here is to generalise the results so they apply to ALL graphs in a particular family. The authors work through the standard graphs, cycles, paths, wheels, trees and complete graphs giving results when known and open problems or conjectures for as yet undiscovered material. The book also contains many illustrations so that if decyphering mathematical reasoning is not your thing, you can gain an understanding from an example of the labelling. The reasoning and proofs in this book give access to the tools to work in the field and so make it ideal for an undergraduate or Honours level text in graph theory and graph labelling. The book provides sufficient definitions and explanations to make it accessible to people with no more than high school mathematics. However, as indicated earlier, the book can also be read in a lighter vein allowing it to be appreciated by those who enjoy puzzles, solving problems or tackling challenges.
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