Die Theorie der regularen Graphen (The Theory of Regular Graphs),
written by the Danish Mathematician Julius Petersen in 1891, is often
considered the first strictly theoretical paper dealing with graphs. In
the 130 years since then, regular graphs have been a common and popular
area of study. While regular graphs are typically considered to be
graphs whose vertices all have the same degree, a more general
interpretation is that of graphs possessing some common characteristic
throughout their structure.
During the past several decades, however, there has been some increased
interest in investigating graphs possessing a property that is, in a
sense, opposite to regularity. It is this topic with which this book
deals, giving rise to a study of what might be called irregularity in
graphs. Here, various irregularity concepts dealing with several topics
in graph theory are described, such as degrees of vertices, graph
labelings, weightings, colorings, graph structures, Eulerian and
Hamiltonian properties, graph decompositions, and Ramsey-type problems.