Langford sequences and a product of digraphs

TL;DR

This paper introduces a novel method combining the $ imes_h$-product and super edge-magic digraphs to generate a vast number of Langford and extended Skolem sequences, enhancing combinatorial sequence construction techniques.

Contribution

It presents a new construction approach for Langford and Skolem sequences using the $ imes_h$-product and super edge-magic digraphs, producing exponential quantities of such sequences.

Findings

Generated exponential numbers of Langford sequences with specific parameters

Extended the construction method to Skolem sequences

Demonstrated applications in combinatorial design theory

Abstract

Skolem and Langford sequences and their many generalizations have applications in numerous areas. The $\otimes_h$-product is a generalization of the direct product of digraphs. In this paper we use the $\otimes_h$-product and super edge-magic digraphs to construct an exponential number of Langford sequences with certain order and defect. We also apply this procedure to extended Skolem sequences.