Computing locating-total domination number in some rotationally symmetric graphs

计算某些旋转对称图中的定位总支配数

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Abstract

Let G = (V, E) be a connected graph. A locating-total dominating set in a graph G is a total dominating set S of a G, for every pair of vertices i, j ∈ V(G)∖S, such that N(i)∩S ≠ N(j)∩S. The minimum cardinality of a locating-total dominating set is called locating-total domination number and represented as γtL. In this paper, locating-total domination number is determined for some cycle-related graphs. Furthermore, some well-known graphs of convex polytopes from the literature are also considered for the locating-total domination number.

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