This book discusses the origin of graph theory from its humble
beginnings in recreational mathematics to its modern setting or
modeling communication networks, as is evidenced by the World Wide
Web graph used by many Internet search engines. The second edition
of the book includes recent developments in the theory of signed
adjacency matrices involving the proof of sensitivity conjecture
and the theory of Ramanujan graphs. In addition, the book discusses
topics such as Pick's theorem on areas of lattice polygons and
Graham-Pollak's work on addressing of graphs. The concept of graph
is fundamental in mathematics and engineering, as it conveniently
encodes diverse relations and facilitates combinatorial analysis of
many theoretical and practical problems. The text is ideal for a
one-semester course at the advanced undergraduate level or
beginning graduate level.
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