Abstract
Given a graph G and an edge e ∈ E ( G ) , let S be a vertex set of G. For any two vertices x, y ∈ S , if e belongs to all the shortest paths between x and y, then x and y can monitor the edge e. For each edge e of G, if there exists x and y in S such that x and y can monitor e, then the set S can be called a monitoring-edge-geodetic ( MEG for short) set of G. The MEG number, denoted by meg ( G ) , is the size of the smallest MEG set of G. In this paper, we obtain the exact values of the MEG numbers for radix triangular mesh networks, Sierpiński graphs, Sierpiński gasket graphs and Sierpiński generalized graphs.
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