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Information Sciences Letters

Information Sciences Letters

Abstract

The commuting graph of a ring R, denoted by Γ (R), is a graph whose vertices are all non-central elements of R and two distinct vertices u and v are adjacent if and only if uv = vu. In this paper let R be the commutative ring with 1R ̸= 0R . In this paper we investigate, some basic properties of Γ (M(m1 ⊕ m2, R)) we find the g(Γ ((M(m1 ⊕ m2, R))) = 3 and we show that Γ ((M(m1 ⊕ m2, R)) is not Eulerian, and Γ((M(m1 ⊕m2,R)) is not planar.

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