%0 Journal Article %A Ziaaddini, M. %A Erfanian, A. %T Relative non-Normal Graphs of a Subgroup of Finite Groups %J Iranian Journal of Mathematical Sciences and Informatics %V 16 %N 1 %U http://ijmsi.ir/article-1-1198-en.html %R %D 2021 %K Non-normal graph, Relative Non-normal graph, Normality degree, Outer planar., %X Let G be a finite 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 HHK and KNK(H) and two vertices x ∈ H HK and y ∈ K NK(H) are adjacent if xy / ∈ H, where HK =Tk∈K Hk and NK(H) = {k ∈ K : Hk = H}. We determined some numerical invariants and state that when this graph is planar or outerplanar. %> http://ijmsi.ir/article-1-1198-en.pdf %P 181-189 %& 181 %! %9 Research paper %L A-10-3071-1 %+ Department of Pure Mathematics and the Center of Excellence in Analysis on Algebraic Structures, Ferdowsi University of Mashhad %G eng %@ 1735-4463 %[ 2021