Counting Matching Numbers in Catacondensed Polyomino Systems

Extremal Values of VDB Topological Indices over Catacondensed Polyomino Systems

A VDB topological index is defined as

Extremal Matching Energy of Random Polyomino Chains

Polyomino graphs is one of the research objectives in statistical physics and in modeling problems of surface chemistry. A random polyomino chain is a subgraph of a polyomino graph. The matching energy is defined as the sum of the absolute values of the zeros of the matching polynomial of a graph. In this paper, we characterize the graphs with the extremal matching energy among all random polyo...

Counting Keith numbers

A Keith number is a positive integer N with the decimal representation a1a2 . . . an such that n ≥ 2 and N appears in the sequence (Km)m≥1 given by the recurrence K1 = a1, . . . ,Kn = an and Km = Km−1 + Km−2 + · · · + Km−n for m > n. We prove that there are only finitely many Keith numbers using only one decimal digit (i.e., a1 = a2 = · · · = an), and that the set of Keith numbers is of asympto...

Numbers and Counting

Counting Square-Free Numbers

The main topic of this contribution is the problem of counting square-free numbers not exceeding n. Before this work we were able to do it in time Õ( √ n). Here, the algorithm with time complexity Õ(n) and with memory complexity Õ(n) is presented. Additionally, a parallel version is shown, which achieves full scalability. As of now the highest computed value was for n = 10. Using our implementa...