Locating-Total Domination Number of Cacti Graphs

Abstract EN

For a connected graph J, a subset W⊆VJ is termed as a locating-total dominating set if for a∈VJ, Na∩W≠ϕ, and for a, b∈VJ−W, Na∩W≠Nb∩W.

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.