For a connected graph J, a subset is termed as a locating-total dominating set if for , and for . The number of elements in a smallest such subset is termed as the locating-total domination number of J. In this paper, the locating-total domination number of unicyclic graphs and bicyclic graphs are studied and their bounds are presented. Then, by using these bounds, an upper bound for cacti graphs in terms of their order and number of cycles is estimated. Moreover, the exact values of this domination variant for some families of cacti graphs including tadpole graphs and rooted products are also determined.

中文翻译：

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仙人掌图的总定位数

对于连通图J，子集 被称为“定位总支配集”，如果 ，并。最小的此类子集中的元素数称为J的定位总支配数。本文研究了单环图和双环图的定位总支配数，并给出了它们的界限。然后，通过使用这些界限，就仙人掌图的顺序和循环数来估计其上限。此外，还确定了针对某些仙人掌图系列（包括t图和生根产品）的该控制变量的确切值。