The Monitoring-Edge-Geodetic Number of Some Planar Networks
Yalong Lei, G.R. Liu, Chenxu Yang, Wenlong Zhao · Journal of Interconnection Networks · 2025
Let [Formula: see text] be a graph with vertex set [Formula: see text] and edge set [Formula: see text]. For any [Formula: see text] and [Formula: see text], if [Formula: see text], then we can say that [Formula: see text] and [Formula: see text] monitor the edge [Formula: see text] in graph [Formula: see text]. A set [Formula: see text] of vertices of [Formula: see text] is monitoring-edge-geodetic set (MEG set for short) of [Formula: see text], if for any edge [Formula: see text], there exist two vertices [Formula: see text] such that [Formula: see text] is monitored by [Formula: see text] and [Formula: see text]. The monitoring-edge-geodetic number (MEG number for short), [Formula: see text], is the cardinality of the minimum MEG set in [Formula: see text]. In this paper, we obtain the monitoring-edge-geodetic number for several well-known networks, included ring network, pyramid network, L-shaped tile and convex polytope variant.