Monitoring-edge-geodetic numbers of radix triangular mesh and Sierpiński graphs

Given a graph G and an edge $ e\in E(G) $ e is an element of E(G), let S be a vertex set of G. For any two vertices x, $ y\in S $ y is an element of 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 ( $ \operatorname {MEG} $ MEG for short) set of G. The $ \operatorname {MEG} $ MEG number, denoted by $ \operatorname {meg}(G) $ meg(G), is the size of the smallest $ \operatorname {MEG} $ MEG set of G. In this paper, we obtain the exact values of the $ \operatorname {MEG} $ MEG numbers for radix triangular mesh networks, Sierpinski graphs, Sierpinski gasket graphs and Sierpinski generalized graphs.