\((k, l)\)-anonymity in wheel-related social graphs measured on the base of \(k\)-metric antidimension (Q2052120)

Summary: For the study and valuation of social graphs, which affect an extensive range of applications such as community decision-making support and recommender systems, it is highly recommended to sustain the resistance of a social graph \(G\) to active attacks. In this regard, a novel privacy measure, called the \((k, l)\)-anonymity, is used since the last few years on the base of \(k\)-metric antidimension of \(G\) in which \(l\) is the maximum number of attacker nodes defining the \(k\)-metric antidimension of \(G\) for the smallest positive integer \(k\). The \(k\)-metric antidimension of \(G\) is the smallest number of attacker nodes less than or equal to \(l\) such that other \(k\) nodes in \(G\) cannot be uniquely identified by the attacker nodes. In this paper, we consider four families of wheel-related social graphs, namely, Jahangir graphs, helm graphs, flower graphs, and sunflower graphs. By determining their \(k\)-metric antidimension, we prove that each social graph of these families is the maximum degree metric antidimensional, where the degree of a vertex is the number of vertices linked with that vertex.