ON DIMENSION OF SOME FINITE ALGEBRAIC GRAPHS OF FINITE RINGS

ON DIMENSION OF SOME FINITE ALGEBRAIC GRAPHS OF FINITE RINGS

M. G. TALESHANI, M. T. LASKUKALAYEH, A. ABBASI

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Abstract. Suppose that ????(Zp1p2


p) is a graph with the vertex set of nonzero zero- divisors of the nite ring Zp1p2:::p, where  > 1, and x ???? y is an edge if and only if x and y are -prime, where  = fp1; p2; : : : ; pg is a set of odd prime numbers and a and b are -prime if either (a; b) = 1 or (a; b) = p, p =2 . In this paper we study dimension, edge metric dimension and fraction dimension of the graph.

Keywords:diameter, distance, metric dimension, decomposition.

AMS Subject Classification:05C12, 05C51, 05C75, 05C90.