# Super Edge-Antimagic Graphs: A Wealth of Problems and Some Solutions

###### Martin Bača and Mirka Miller
Publisher:
Brown Walker Press
Publication Date:
2008
Number of Pages:
227
Format:
Paperback
Price:
28.95
ISBN:
978-1599424651
Category:
Monograph
[Reviewed by
Charles Ashbacher
, on
01/25/2009
]

As a co-editor of the Journal of Recreational Mathematics (JRM), I was even more interested in this book than I would have otherwise been. A magic graph is one that has an edge labeling so that the sum of the edge labelings for each of the vertices is the same. This definition is an extension of the magic square, a staple topic of recreational mathematics. An antimagic graph is one where the edges are labeled with the numbers {1, 2, 3, 4, ... , n} so that the sum of the edge weights on each of the vertices is pairwise distinct. A friendship graph is a set of triangles that have a common vertex but are otherwise disjoint and a labeling is called super if the numbers assigned to the vertices are the smallest possible.

The authors have put together a series of theorems on the graphs satisfying these and other definitions and most of the proofs are included. Conjectures and open problems are interspersed throughout and they are also listed at the end. As I worked my way through the book, I experienced an overwhelming shift to the computer programmer side of my brain. I began thinking of ways in which the graphs could be represented in memory and how systematic and Monte Carlo testing of the unsolved problems could be done.

When my computer programming side was again rendered dormant, I began thinking of problems of these types that could be created for the problem column of JRM. All of this mental wandering makes this one of the most unusual books that I have read, for while reading it I had to force myself to stop thinking and read it.

Charles Ashbacher splits his time between consulting with industry in projects involving math and computers, teaching college classes and co-editing The Journal of Recreational Mathematics. In his spare time, he reads about these things and helps his daughter in her lawn care business.