Let V be the set of vertex of a graph G. The set S is a dominating set, being a subset of the set V, if every vertex in the set V is in the set S, or if it is neighbor of a vertex in the set S. The number of elements of the set S with the least number of elements is the dominating number of graph G. In this study, we have worked on a type of dominating called porous exponential domination. In this new parameter, while the distance between vertex s and vertex v grows this weight value reduces exponentially. If all vertices in S dominate all vertices of G a with a total weight of at least 1, the set S is named as a porous exponential dominating set of graph G. The cardinality of the set with the least number of elements of the obtained porous exponential domination sets is defined as the porous exponential domination number of graph G. In this paper we compute the porous exponential domination number of the R − graphs under corona and join product.

中文翻译：

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复合网络中距离支配的一种变化

令V为图G的顶点集合。如果集合V中的每个顶点都在集合S 中，或者如果它是集合S中某个顶点的邻居，则集合S是支配集合，是集合V 的子集。集合S中元素数量最少的元素数量是图G的主导数量。在这项研究中，我们研究了一种称为多孔指数支配的支配类型。在这个新参数中，当顶点s和顶点v之间的距离增加时，该权重值呈指数下降。如果S中的所有顶点支配G a 的所有顶点，并且总权重至少为 1，则集合S被称为图G的多孔指数支配集。将得到的多孔指数支配集合中元素数量最少的集合的基数定义为图G的多孔指数支配数。在本文中，我们计算了电晕和连接积下R  − 图的多孔指数支配数。