On the zero-divisor Cayley graph of a finite commutative ring
AR Naghipour - Iranian Journal of Mathematical Sciences and …, 2017 - ijmsi.ir
Iranian Journal of Mathematical Sciences and Informatics, 2017•ijmsi.ir
Let R be a fnite commutative ring and N (R) be the set of non unit elements of R. The non
unit graph of R, denoted by Gamma (R), is the graph obtained by setting all the elements of
N (R) to be the vertices and defning distinct vertices x and y to be adjacent if and only if x-yin
N (R). In this paper, the basic properties of Gamma (R) are investigated and some
characterization results regarding connectedness, girth and planarity of Gamma (R) are
given.
unit graph of R, denoted by Gamma (R), is the graph obtained by setting all the elements of
N (R) to be the vertices and defning distinct vertices x and y to be adjacent if and only if x-yin
N (R). In this paper, the basic properties of Gamma (R) are investigated and some
characterization results regarding connectedness, girth and planarity of Gamma (R) are
given.
Abstract
Let R be a fnite commutative ring and N (R) be the set of non unit elements of R. The non unit graph of R, denoted by Gamma (R), is the graph obtained by setting all the elements of N (R) to be the vertices and defning distinct vertices x and y to be adjacent if and only if x-yin N (R). In this paper, the basic properties of Gamma (R) are investigated and some characterization results regarding connectedness, girth and planarity of Gamma (R) are given.
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