Monitoring edge-geodetic numbers of convex polytopes and four networks

Abstract

Foucard, Krishna and Lekshmi introduced a new graph-theoretic concept in the area of network monitoring. Let G be a graph with vertex set , there exists a subset , if deleting any edge in G, one can find that there exist at least two vertices in S whose distance is changed, then we call S is a monitoring edge-geodetic set (MEG-set for short). The minimum size of the MEG-set of G is called the monitoring edge-geodetic number of G (meg(G) for short). In this paper, we study the monitoring edge-geodetic number of some well-known networks, including Ladder, butterfly, circulant and Benes networks and convex polytopes.