Let G be a group and Zn(G) be the n-th term of upper central series of G, for every n ≥ 1. The n-th central graph of G denoted by Γn z (G) is a simple graph whose vertices are elements of G and two distinct vertices x and y are adjacent if xy ∈ Zn(G). If n = 1, then we get the known central graph which was introduced by Balakrishnan and Sattanathan [ 3 ]. We study the structure of Γn z (G) and determine some numerical invariants such as dominating, chromatic and independence numbers which are all mostly new or an improvement of results given for the central graph. Moreover, we state some conditions under which Γn z (G) is isomorphic to the Cayley graph Cay(G,Zn(G)/e).

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