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2011•Involve a Journal of MathematicsOpen access

Five-point zero-divisor graphs determined by equivalence classes

Florida Victoria Levidiotis, Sandra Spiroff

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Abstract

Five-point zero-divisor graphs determined by equivalence classesFlorida Levidiotis and Sandra Spiroff (Communicated by Scott Chapman)We study condensed zero-divisor graphs (those whose vertices are equivalence classes of zero-divisors of a ring R) having exactly five vertices.In particular, we determine which graphs with exactly five vertices can be realized as the condensed zero-divisor graph of a ring.We provide the rings for the graphs which are possible, and prove that the rest of graphs can not be realized via any commutative ring.There are 34 graphs in total which contain exactly five vertices.MSC2000: primary 13A99; secondary 05C99.Keywords: condensed zero-

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Five-point zero-divisor graphs determined by equivalence classesFlorida Levidiotis and Sandra Spiroff (Communicated by Scott Chapman)We study condensed zero-divisor graphs (those whose vertices are equivalence classes of zero-divisors of a ring R) having exactly five vertices.In particular, we determine which graphs with exactly five vertices can be realized as the condensed zero-divisor graph of a ring.We provide the rings for the graphs which are possible, and prove that the rest of graphs can not be realized via any commutative ring.There are 34 graphs in total which contain exactly five vertices.MSC2000: primary 13A99; secondary 05C99.Keywords: condensed zero-

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Five-point zero-divisor graphs determined by equivalence classesFlorida Levidiotis and Sandra Spiroff (Communicated by Scott Chapman)We study condensed zero-divisor graphs (those whose vertices are equivalence classes of zero-divisors of a ring R) having exactly five vertices.In particular, we determine which graphs with exactly five vertices can be realized as the condensed zero-divisor graph of a ring.We provide the rings for the graphs which are possible, and prove that the rest of graphs can not be realized via any commutative ring.There are 34 graphs in total which contain exactly five vertices.MSC2000: primary 13A99; secondary 05C99.Keywords: condensed zero-

Key concepts: Mathematics, Zero (linguistics), Zero divisor, Equivalence (formal languages), Divisor (algebraic geometry), Combinatorics, Point (geometry), Discrete mathematics

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