k,l-Anonymity in Wheel-Related Social Graphs Measured on the Base of k-Metric Antidimension

Abstract

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.