On zero divisor graphs of the rings
For a commutative ring R with non-zero zero-divisor set Z^*(R) Z∗(R), the zero-divisor graph
of R is\varGamma (R) Γ (R) with vertex set Z^*(R) Z∗(R), where two distinct vertices x and y
are adjacent if and only if xy= 0 xy= 0. The zero-divisor graph structure of Z _ p^ n Z pn is
described. We determine the clique number, degree of the vertices, size, metric dimension,
upper dimension, automorphism group, Wiener index of the associated zero-divisor graph of
Z _ p^ n Z pn. Further, we provide a partition of the vertex set of\varGamma (Z _ p^ n) Γ (Z …
of R is\varGamma (R) Γ (R) with vertex set Z^*(R) Z∗(R), where two distinct vertices x and y
are adjacent if and only if xy= 0 xy= 0. The zero-divisor graph structure of Z _ p^ n Z pn is
described. We determine the clique number, degree of the vertices, size, metric dimension,
upper dimension, automorphism group, Wiener index of the associated zero-divisor graph of
Z _ p^ n Z pn. Further, we provide a partition of the vertex set of\varGamma (Z _ p^ n) Γ (Z …
Abstract
For a commutative ring R with non-zero zero-divisor set , the zero-divisor graph of R is with vertex set , where two distinct vertices x and y are adjacent if and only if . The zero-divisor graph structure of is described. We determine the clique number, degree of the vertices, size, metric dimension, upper dimension, automorphism group, Wiener index of the associated zero-divisor graph of . Further, we provide a partition of the vertex set of into distance similar equivalence classes and we show that in this graph the upper dimension equals the metric dimension. Also, we discuss similar properties of the compressed zero-divisor graph.
Springer