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

Given a graph G and an edge $ e\in E(G) $ e ∈ E (G) , let S be a vertex set of G. For any two vertices x, $ y\in S $ 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 ( $ \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, Sierpiński graphs, Sierpiński gasket graphs and Sierpiński generalized graphs. [ABSTRACT FROM AUTHOR]