Graphs embedded in an oriented surface that satisfy a special combinatorial condition allow to define a mapping class of the surface with support in any tubular neighborhood of the graph. The classical right Dehn twist is most basic example. The restriction of these mapping classes to closed regular tubular neighborhoods are the building blocks for Milnor monodromies of isolated curve singularities on normal surfaces. Such restrictions composed with one left Dehn twist are interesting pseudo-Anosov diffeomorphisms. The content of the course is based on work of Christian Graf, Pablo Portilla Cuadrado, Baldur Sigurdsson, Maria Pe Pereira, Javier Fernandez de Bobadilla and the author.