Security in Sierpinski graphs

A secure set S subset of V of a graph G = (V, E) is a set whose every nonempty subset can be successfully defended from an attack, under appropriate definitions of 'attack' and 'defense'. The set S is secure when vertical bar N[X]boolean AND S vertical bar >= vertical bar N[X] - S vertical bar for every X subset of S. A set S subset of V is secure dominating if it is both secure and dominating. The minimum cardinality of a secure set in G is the security number of G, s(G), and the minimum cardinality of a secure-dominating set in G is the secure domination number of G, gamma(s)(G). In this paper, we initiate a study of these parameters in the well-known Sierpinski graphs. (c) 2022 Elsevier B.V. All rights reserved.