This book has been recommended to me by a guiding hand/mentor mathematician when I showed interest in his field, and he seemed to really like this book however he doesn't really know me and my mathematical maturity (could be over-estimating or under-estimating).

Extra details:

I've read a little of Béla Bollobás' random graph theory and could follow perhaps a quarter of what I'd seen. I still mix up "Hamiltonian Path" and "Eulerian Path", so I'm wondering if I need to re-master my intro. discrete maths content before reading The Petersen Graph, or could I just dive in and look up whatever I'm dodgy on.

I'm aware that some books have innocuous titles like "Graph Theory" and turn out to be extremely dense and terse, taking several courses before you can make much progress. I'm a dodgy undergrad who's a bit rusty, and never gotten into combinatorics. I'm not quite expecting this book to be a transformative experience, but I hope for considerable enrichment (are these expectations too high?). I've done the basics of complex analysis, group theory and linear algebra.

I've perused the first pages of many maths books, only to be left in the dust when things go from 1 to 100 real fast. Is there a good way to see whether this might happen without actually reading the book until you hit a wall (not enough background material for instance)? If one doesn't know the particular books in question, it can be tricky to open Spivak Calculus expecting a watered-down high-school style expose rather than an intro to analysis.

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    $\begingroup$ This sounds more like a question about learning math which might be appropriate for math.stackexchange.com. Do you think you can reframe it so it is more about teaching? $\endgroup$ – kcrisman Sep 13 '19 at 2:52
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    $\begingroup$ Also, I can't find the book you are referring to. Is it possibly this one (just a guess, sorry if I got it wrong)? amazon.com/Petersen-Australian-Mathematical-Society-Lecture/dp/… In that case you should probably edit the title since otherwise people will find it difficult to help. $\endgroup$ – kcrisman Sep 13 '19 at 2:53
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    $\begingroup$ I suggest "Applied Combinatorics" (any of the editions) by Alan Tucker. $\endgroup$ – Benjamin Dickman Sep 14 '19 at 15:32
  1. There are no Amazon reviews. Doesn't seem like a popular title. (Just an indicator, not a Euclidean proof...but a negative note.)

  2. The preface says that it is approaching teaching all of graph theory via this one graph as motivation. Seems rather non-standard. Again, not Euclidean proof, but a negative indicator.

  3. If you are self studying AND a weak student (really either of those, but especially with both), I recommend to go with the easiest, clearest text possible. You can always go back later and repeat with a harder one. But start with easiest path.

  4. I reccommend this text: https://www.amazon.com/Introduction-Graph-Theory-Dover-Mathematics/dp/0486678709/ Very easy--in fact the criticism is that it doesn't cover enough. But that's a feature, not a bug, at this point. Very well reviewed (in number and score). Cheap. Old and somewhat standard in approach.

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