Abstract :
By applying a sequence of edge-gluings on a set of cycles each of length k, we obtain a special series-parallel graph. The well-known k-gon tree theorem (see [1,10]) states that these graphs form a ξ-equivalence class. Many of the other known classes of ξ-unique graphs and ξ-equivalence classes are also special cases of series-parallel graphs. This paper introduces some new chromatic invariants for this class of graphs. We illustrate the usefulness of these invariants by constructing several new ξ-equivalence classes which include edge-gluings of graphs in a special class of series-parallel graphs. The latter result parallels that of the k-gon tree theorem.
