Conference Information Technologies - Applications and Theory, ITAT 2024

In this paper, we focus on integer sequences corresponding to the number of vertices in 𝑘-iterated line digraphs. We begin by introducing the core concepts related to digraphs. Then, we describe a method, proposed by Dalfó and Fiol, for calculating the order of 𝑘-iterated line digraphs. We explore various families of digraphs, such as De Bruijn, Kautz, Cyclic Kautz, and Square-free digraphs. To generate integer sequences representing the number of vertices in 𝑘-iterated line digraphs, we implement an algorithm that constructs induced subdigraphs by not allowing vertices containing forbidden subwords. The results include comparisons of the obtained integer sequences with those in the OEIS database and identification of new integer sequences. Our algorithm is implemented in the computational system GAP.