Damghan UniversityGlobal Analysis and Discrete Mathematics2476-53417220220901On Invariant Graph Of Γ-Near-Ring14515029610.22128/gadm.2022.582.1076ENElahehKhamsehDepartment of mathematics, Islamic Azad university, Shahr-e-Qods Branch, Tehran, Iran.Journal Article20220721Let <em>U</em> be an invariant subset of finite <em>Γ</em>-near-ring M. There are many papers that consider the graph respect to the near-ring and the interplay between algebraic structures and graphs are studied. Indeed, it is worthwhile to relate algebraic properties of near-ring to the combinatorics properties of assigned graphs. In this paper the graph with respect to an invariant subset <em>U</em> of <em>Γ</em>-near-ring <em>M</em>, denoted by <em>Γ <sup>α</sup> <sub>U</sub> (M)</em> is introduced and the basic properties of it is investigated. Also the relation between the commutativity of <em>M</em> and properties of this graph is presented.https://gadm.du.ac.ir/article_296_89bbaf346995e5fcbd1776f928f16e01.pdf