We examine some properties of the 2-variable greedoid polynomial f(G;t, z) when G is the branching greedoid associated to a rooted graph or a rooted directed graph. For rooted digraphs, we show a factoring property of f (G;t ,z) determines whether or not the rooted digraph has a directed cycle.

We present an approach for programming with graph transformation rules in which programs can be as efficient as programs in imperative languages. The basic idea is to equip rules and host graphs with distinguished nodes, so-called roots, and to match roots in rules with roots in host graphs. This enables graph transformation rules to be matched in constant time, provided that host graphs have a...

In this paper, we consider an arbitrary class H of rooted graphs such that each biconnected component is given by a representation with reflectional symmetry, which allows a rooted graph to have several different representations, called embeddings. We give a general framework to design algorithms for enumerating embeddings of all graphs in H without repetition. The framework yields an efficient...

A mandibular fi rst molar with two distal roots is an interesting example of anatomic variation. This paper describes case reports of mandibular fi rst molar with three roots (one mesial and two distal) and four canals (two in mesial and one in each distobuccal and distolingual root). The canals were shaped with protaper rotary fi les and irrigated with 5.25% sodium hyochlorite, 0.2 %w/v of chl...

A stationary random graph is a random rooted graph whose distribution is invariant under re-rooting along the simple random walk. We adapt the entropy technique developed for Cayley graphs and show in particular that stationary random graphs of subexponential growth are almost surely Liouville, that is, admit no non constant bounded harmonic functions. Applications include the uniform infinite ...