The vertex set $L \subseteq V (G)$ is a liar's dominating set if and only if it satisfies the following two conditions: (i) $L$ double dominates every \(v \in V (G)\) and (ii) for every pair \(u, v\) of distinct vertices, \( \vert (N[u] \cup N[v]) \cap L \vert \geq 3\). The liar's domination number for a graph \(G\) is denoted by \(\gamma_L (G)\) which is the minimum cardinality of the liar's dominating set \(L\). Liar's domination was introduced by P. J. Slater. In a liar's dominating set it is assumed that any one protective device in its neighborhood of the intruder vertex might misreport the location of an intruder vertex in its closed neighborhood. In this paper, we determine the liar's domination set for Sierpi\'nski-like graphs.
Keywords and Phrases
Domination, Liar's domination, Sierpi\'nski graphs, Sierpi\'nski cycle graphs, Sierpi\'nski complete graphs.
A.M.S. subject classiﬁcation