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This textbook acts as a pathway to higher mathematics by seeking
and illuminating the connections between graph theory and diverse
fields of mathematics, such as calculus on manifolds, group theory,
algebraic curves, Fourier analysis, cryptography and other areas of
combinatorics. An overview of graph theory definitions and
polynomial invariants for graphs prepares the reader for the
subsequent dive into the applications of graph theory. To pique the
reader's interest in areas of possible exploration, recent results
in mathematics appear throughout the book, accompanied with
examples of related graphs, how they arise, and what their valuable
uses are. The consequences of graph theory covered by the authors
are complicated and far-reaching, so topics are always exhibited in
a user-friendly manner with copious graphs, exercises, and Sage
code for the computation of equations. Samples of the book's source
code can be found at
github.com/springer-math/adventures-in-graph-theory. The text is
geared towards advanced undergraduate and graduate students and is
particularly useful for those trying to decide what type of problem
to tackle for their dissertation. This book can also serve as a
reference for anyone interested in exploring how they can apply
graph theory to other parts of mathematics.
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