Gordon and McMahon defined a two-variable greedoid polynomial f(G; t, z) for any G. They studied polynomials greedoids associated with rooted graphs digraphs. proved that of digraphs have the multiplicative direct sum property. In addition, these are divisible by $$1 + z$$ under certain conditions. We compute all up to order six. A is said factorise if it has non-constant factor lower degree. s...

In this paper, we investigate a parking process on uniform random rooted plane tree with $n$ vertices. Every vertex of the has space for single car. Cars arrive at independent uniformly vertices tree. If is unoccupied when car arrives there, it parks. not, drives towards root and parks in first empty encounters (if there one). We are interested asymptotics probability event that all cars can pa...

We present an expected polynomial time algorithm to generate an unlabeled connected cubic planar graph uniformly at random. We first consider rooted connected cubic planar graphs, i.e., we count connected cubic planar graphs up to isomorphisms that fix a certain directed edge. Based on decompositions along the connectivity structure, we derive recurrence formulas for the exact number of rooted ...

Whereas biologists might think of rooted trees as the natural, or even the only, way to display phylogenetic relationships, this is not the case for a mathematician, to whom rooted and unrooted trees are graph-theoretical constructions that can be transformed easily into one another. An unrooted tree contains the same information as its rooted counterpart with the single exception that it does ...