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- W4224300912 abstract "Let R be a commutative ring with Z(R) its set of all zero-divisors. The new extension of zero-divisor graph of a commutative ring R denoted by Γ˜(R), is an undirected graph with vertex set Z(R)* and two vertices x and y are adjacent if and only if either xy = 0 or x+y∈Z(R). In this paper, first we characterized finite rings R for which Γ˜(R), is isomorphic to some well-known graphs and then we classify all the finite rings R for which Γ˜(R) is planar, outerplanar, toroidal or double toroidal. Finally, we classify the finite rings R for which the graph Γ˜(R) has crosscap at most two." @default.
- W4224300912 created "2022-04-26" @default.
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- W4224300912 date "2022-01-02" @default.
- W4224300912 modified "2023-10-03" @default.
- W4224300912 title "On the planarity, genus and crosscap of new extension of zero-divisor graph of commutative rings" @default.
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- W4224300912 doi "https://doi.org/10.1080/09728600.2022.2058437" @default.
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