Eternal and Secure Domination in Graphs
Mobile guards on the vertices of a graph are used to defend it against attacks that occur in sequence on its vertices. Various models for this problem have been proposed. In this chapter, we describe a number of these models with particular attention to two general cases (i) when the attack sequence is infinitely long and the guards must induce a dominating set before and after each attack, the so-called eternal domination and (ii) when the attack sequence consists of one attack and the guards must induce a dominating set before and after the attack, the so-called secure domination. Results from the literature concerning the number of guards needed to successfully defend a graph in each of these problems are surveyed. Several conjectures and open problems are presented.
Developments in Mathematics
Digital Object Identifier (DOI)
Klostermeyer, W.F., Mynhardt, C.M. (2020) Eternal and Secure Domination in Graphs. Developments in Mathematics, 64, 445-478.