Graph theory (drawing) references

I have just finished reading "Graph Drawing" by di Battista, Eades,
Tamassia & Tollis (Prentice Hall) and have found the book to be of
little help to beginners like me.

The algorithms are stated broadly and then you are referred to
(unavailable to me) literature.

Specificially, I am interested in algorithms for determining if the
graph is a tree, if it is st-graph, if it is biconnected, planar, etc.

Only after such determination can the above-mentioned book be
(moderately) useful for actual implementation of some drawing
algorithm.

I would very much appreciate references that do not include obscure and
expensive journals.

Tony

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