Faculty of Mathematics, Physics
and Informatics
Comenius University Bratislava

Seminar of Graph Theory - Dominika Mihálová (4.4.2024)

Thursday 4.4.2024 at 9:50, Lecture room C

02. 04. 2024 13.10 hod.
By: Martin Škoviera

Dominika Mihálová:
On digraphs and their iterated line digraphs

In my presentation, I will report on the project I participated on during the mobility stay on University of Lleida. In that project, we study inner metric parameters of digraphs (such as inner diameter, inner radius, ...) and how these values change considering the line digraph of the considered digraph. Our focus is also on integer sequences that are generated by inner metric parameters of iterated line digraphs. We show recurrence relation for the number of vertices in k-iterated line digraph. With the recurrence equation, we are able to solve a problem of finding the number of words over a given alphabet by avoiding a given set of subwords. The results are shown on the graph families, whose vertices are represented as words over some finite alphabet: De Bruijn, Kautz, Cyclic-Kautz, Square-Free.

Joint work with N. H. Bong, C. Dalfó, and M. A. Fiol

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