Combinatorial classes T that are recursively defined using combinations of the standard multiset, sequence, directed cycle and cycle constructions, and their restrictions, have generating series T(z) with a positive radius of convergence; for most of these a simple test can be used to quickly show that the form of the asymptotics is the same as that for the class of rooted trees: C · ρ−n · n−3/...

A cycle basis in an undirected graph is a minimal set of simple cycles whose symmetric differences include all Eulerian subgraphs of the given graph. We define a rooted cycle basis to be a cycle basis in which all cycles contain a specified root edge, and we investigate the algorithmic problem of constructing rooted cycle bases. We show that a given graph has a rooted cycle basis if and only if...

This paper discusses the notion of projectivity and algorithms for projectivizing and detecting non-projective edges in totally ordered rooted trees (such trees are used in dependency syntax analysis of natural language, where they are called dependency trees). In the first part, we review the notion of projectivity, then we present a new definition inspired by the algorithmic inquiry and show ...

AIM To analyse the anatomy of the root canal system of maxillary premolars with three distinct roots using high-resolution computed tomography (μCT). METHODOLOGY Ten three-rooted human maxillary premolars were scanned transversally from crown to apex at 42μm intervals using a high-resolution desktop μTC system (Skyscan 1072). The images were processed and analysed for the following features: ...

• Mediterranean-type ecosystems contain 20% of all vascular plant diversity on Earth and have been identified as being particularly threatened by future increases in drought. Of particular concern is the Cape Floral Region of South Africa, a global biodiversity hotspot, yet there are limited experimental data to validate predicted impacts on the flora. In a field rainout experiment, we tested w...

This paper concerns counting the imbeddings of a graph in a surface. In the first installment of our current work, we showed how to calculate the genus distribution of an iterated amalgamation of copies of a graph whose genus distribution is already known and is further analyzed into a partitioned genus distribution (which is defined for a double-rooted graph). Our methods were restricted there...

A set of vertices W resolves a graph G if every vertex of G is uniquely determined by its vector of distances to the vertices in W . The metric dimension for G, denoted by dim(G), is the minimum cardinality of a resolving set of G. In order to study the metric dimension for the hierarchical product G2 2 uG1 1 of two rooted graphs G2 2 and G u1 1 , we first introduce a new parameter, the rooted ...