On Counting

On Counting Polynomials of Some Nanostructures

The Omega polynomial(x) was recently proposed by Diudea, based on the length of strips in given graph G. The Sadhana polynomial has been defined to evaluate the Sadhana index of a molecular graph. The PI polynomial is another molecular descriptor. In this paper we compute these three polynomials for some infinite classes of nanostructures.

Counting on

On the Means of the Values of Prime Counting Function

In this paper, we investigate the means of the values of prime counting function $pi(x)$. First, we compute the arithmetic, the geometric, and the harmonic means of the values of this function, and then we study the limit value of the ratio of them.

On counting planar embeddings

A method for counting the embeddings of a connected but not necessarily biconnected planar graph is given. The method relates the embedding of edges around an articulation point to a tree structure called an embedding tree. MacLane [S] gives a method for counting the number of distinct embeddings of a biconnected planar graph. This method is based on a decomposition into triconnetted components...

Counting maps on doughnuts

Abstract. How many maps with V vertices and E edges can be drawn on a doughnut with G holes? I solved this problem for doughnuts with up to 10 holes, and my colleagues Alain Giorgetti and Alexander Mednykh counted maps by number of edges alone on doughnuts with up to 11 holes. This expository paper outlines, in terms meant to be understandable by a nonspecialist, the methods we used and those u...