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For r ∈ R, r > 1 and n ∈ Z + , the divisor function σ −r is defined byIn this paper we show the number C r of connectedwhere π(t) is the number of primes p ≤ t. We also show that C r does not take all integer values, specifically that it cannot be equal to 4.

Let G(V, E) be a connected simple undirected graph. In this paper we prove that the edge metric dimension (introduced by Kelenc, Tratnik and Yero) of the Erdős-Rényi random graph G(n, p) is given by: edim (G(n, p)where q = 1 − 2p(1 − p) 2 (2 − p).

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