Monitoring edge-geodetic sets: Hardness and graph products
نویسندگان
چکیده
Foucaud, Krishna and Ramasubramony Sulochana recently introduced the concept of monitoring edge-geodetic sets in graphs, a related graph invariant. These are vertices such that removal any edge changes distance between some pair set. They studied minimum possible size set given graph, which we call number. We show decision problem for number is NP-complete. also give best-possible upper lower bounds Cartesian strong products two graphs. establish exact value many cases, including new examples graphs whose only whole vertex
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2023
ISSN: ['1872-6771', '0166-218X']
DOI: https://doi.org/10.1016/j.dam.2023.06.033