Some inner metric parameters of a digraph: Iterated line digraphs and integer sequences

TL;DR

This paper explores properties of digraphs related to their line digraphs, introducing new concepts like inner diameter and inner radius, and characterizing integer sequences arising from these parameters.

Contribution

It introduces the concepts of inner diameter and inner radius, and provides a method to characterize integer sequences related to iterated line digraphs.

Findings

Characterization of strongly connected digraphs with equal diameters to their line digraphs

Development of a method to identify integer sequences from iterated line digraph parameters

Presentation of new integer sequences not listed in existing databases

Abstract

In this paper, we first give a new result characterizing the strongly connected digraphs with a diameter equal to that of their line digraphs. Then, we introduce the concepts of the inner diameter and inner radius of a digraph and study their behaviors in its iterated line digraphs. Furthermore, we provide a method to characterize sequences of integers (corresponding to the inner diameter or the number of vertices of a digraph and its iterated line digraphs) that satisfy some conditions. Among other examples, we apply the method to the cyclic Kautz digraphs, square-free digraphs, and the subdigraphs of De Bruijn digraphs. Finally, we present some tables with new sequences that do not belong to The On-Line Encyclopedia of Integer Sequences.