Customer Reviews

Graph Theory (Wiley Series in Discrete Mathematics and Optimization)

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Merris has tried to write a text suitable for a one-semester introduction to graph theory for undergraduates with little background required (merely standard proof techniques). He has succeeded in writing a text that can be covered in one term, if you rush, rush, and rush some more. However, he has relegated some important topics to poorly-written exercises (e.g., Euler tours and such). The text also lacks cohesiveness. The Preface makes it clear that Merris wants the book to lead to four independent strands after the initial three chapters. However, a single chapter does not constitute a "strand" to be followed, and the only set of chapters that becomes cohesive at the end is 7, 8, and 9. Regarding chapter 9, don't let the title "Oriented Graphs" mislead you. A tiny portion of the chapter deals with oriented graphs as an excuse to introduce the vertex-edge incidence matrix and then the Laplacian matrix, and the rest of the chapter is devoted to properties of the Laplacian spectrum.

Another complaint is that this text brushes over multigraphs and doesn't even think of talked about digraphs beyond the dumbing-down of digraphs to oriented graphs in chapter 9.

The author's writing style is clear and student-friendly, and the chapters have a good selection of exercises. However, instructors should do the exercises before assigning them, as we encountered at least one unprovable proposition that was simply stated as "Show that ..." There is also at least one statement that is much more difficult than Merris intended.

I think that future editions of this text could have some promise, but it needs work.