There are so many ways to construct graphs from algebraic structures. Most popular constructions are Cayley graphs, commuting graphs and non-commuting graphs from finite groups and zero-divisor graphs and total graphs from commutative rings. For a commutative ring R with non-zero identity, we denote the set of zero-divisors and unit elements of R by Z ( R ) and U ( R ) , respectively. One of the associated graphs to a ring R is the zero-divisor graph; it is a simple graph with vertex set Z ( R ) ? { 0 } , and two vertices x and y are adjacent if and only if x y = 0 . This graph was first introduced by Beck, where all the elements of R are considered as the vertices. Anderson and Badawi, introduced the total graph of R , as the simple graph with all elements of R as vertices, and two distinct vertices x and y are adjacent if and only if x + y ∈ Z ( R ) . For a given graph G , the concept of connectedness, diameter and girth are always of great interest. Several authors extensively studied about the zero-divisor and total graphs from commutative rings. In this paper, we present a survey of results obtained with regard to distances in zero-divisor and total graphs.
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机译：从代数结构构造图的方法有很多。最受欢迎的构造是有限群的Cayley图，交换图和非交换图，交换环的零除数图和总图。对于具有非零同一性的交换环R，我们分别用Z（R）和U（R）表示R的零除数和单位元素的集合。环R的关联图之一是零除数图;它是顶点集为Z（R）的简单图吗？ {0}，并且当且仅当x y = 0时，两个顶点x和y相邻。该图由Beck首次引入，其中R的所有元素均被视为顶点。 Anderson和Badawi将R的总图作为简单图引入，其中R的所有元素均为顶点，并且当且仅当x + y∈Z（R）时，两个不同的顶点x和y相邻。对于给定的曲线图G，连通性，直径和周长的概念总是很受关注。几位作者广泛研究了交换环的零除和总图。在本文中，我们对零除数和总图中的距离所获得的结果进行了调查。
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