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Abstract. This paper is a continuation for the study of the zero-divisor graph for the ring of Gaussian integers modulo n, ‫ޚ(‬ n [i] Let n be a natural number and let < n > be the principal ideal generated by n in ‫ [ޚ‬i]. Then the factor ring

Let R be a commutative finite principal ideal ring with unity, and let G(R) be the simple graph consisting of nontrivial proper ideals of R as vertices such that two vertices I and J are adjacent if they have nonzero intersection. In this paper we continue the work done by Abu Osba. We calculate the radius, eccentricity, domination number, independence number, geodetic number, and the hull number for this graph. We also determine when G(R) is chordal. Finally, we study some properties of the complement graph of G(R).

A diametrical graphGis said to be symmetric ifd(u,v)+d(v,u¯)=d(G)for allu,v∈V(G), whereu¯is the buddy ofu. If moreover,Gis bipartite, then it is called anS-graph. It would be shown that the Cartesian productK2×C6is not only the uniqueS-graph of order12and diameter4, but also the unique symmetric diametrical graph of order12and diameter4.

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