  Tree-width and path-width are well-known graph parameters. Many NP-hard graph
problems allow polynomial-time solutions, when restricted to graphs of bounded
tree-width or bounded path-width. In this work, we study the behavior of
tree-width and path-width under various unary and binary graph transformations.
Doing so, for considered transformations we provide upper and lower bounds for
the tree-width and path-width of the resulting graph in terms of the tree-width
and path-width of the initial graphs or argue why such bounds are impossible to
specify. Among the studied, unary transformations are vertex addition, vertex
deletion, edge addition, edge deletion, subgraphs, vertex identification, edge
contraction, edge subdivision, minors, powers of graphs, line graphs, edge
complements, local complements, Seidel switching, and Seidel complementation.
Among the studied, binary transformations we consider the disjoint union, join,
union, substitution, graph product, 1-sum, and corona of two graphs.
