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arXiv · 2409.02125

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

N. H. Bong·C. Dalfó·M. A. Fiol·D. Závacká
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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.

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N. H. Bong, C. Dalfó, M. A. Fiol, D. Závacká. 2024-09-01. Some inner metric parameters of a digraph: Iterated line digraphs and integer sequences. https://arxiv.org/abs/2409.02125

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