Abstract. Let G be a nite group and H,K be two subgroups of G. We introduce the relative non-normal graph of K with respect to H , denoted by NH;K, which is a bipartite graph with vertex sets HnHK and KnNK-H- and two vertices x 2 HnHK and y 2 KnNK-H- are adjacent if xy =2 H, where HK = T k2K Hk and NK-H- = fk 2 K : Hk = Hg. We determined some numerical invariants and state that when this graph is planar or outerplanar.

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