Year: 2025
Type: article
Abstract: A geodesic cover, also known as an isometric path cover, of a graph is a set of geodesics which cover the vertex set of the graph. An edge geodesic cover of a graph is a set of geodesics which cover the edge set of the graph. The geodesic (edge) cover number of a graph is the cardinality of a minimum (edge) geodesic cover. The (edge) geodesic cover problem of a graph is to find the (edge) geodesic cover number of the graph. Surprisingly, only partial solutions for these problems are available for most situations. In this paper we demonstrate that the geodesic cover number of the $r$-dimensional butterfly is $\lceil (2/3)2^r\rceil$ and that its edge geodesic cover number is $2^r$.
Source: Fundamenta Informaticae
DOI: 10.46298/fi.10201
Institutions: Kuwait University, Shiv Nadar University, Chennai
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: bronze
Funder: Kuwait University
OpenAlex ID: W4415596243
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