The Gutman Index of the Zero-divisor Graph on the Commutative Ring Zn
A zero-divisor graph over a commutative ring is an undirected simple connected graph,whose vertex set is the set of zero factors over the ring.Based on the Gutman index of degree and distance,the method of classification discussion is mainly adopted in this paper.Firstly,the vertex of the zero-divisor graph on the ring is divided.Secondly,the degree and distance on the induced sub-graphs of the zero-divisor graph and the connection relationship between them are discussed.Thus the Gutman index of the zero-di-visor graph in some cases is described.
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