Liar’s Domination in Generalized Petersen Graphs

Abstract

Domination in graphs has been a widely researched topic and has numerous applications in science and engineering. One of the variations of domination is the liar's domination and it was introduced by P.J. Slater. Here, a network is showed as a graph and all of its vertices are probably the possible locations for the intruder to enter the network. The dominating set is a set of protection devices placed at a vertex so as to detect the intruder and its exact location in its closed neighbourhood even if one protection device is allowed to lie or becomes faulty. Many authors have arrived remarkable results in several graphs. The generalized Petersen graph is a well-organized small network when we consider its node degree, diameter, and network size. Considering the generalized Petersen graphs several network topologies have been suggested and explored. Here, we find the liar's domination number for generalized Petersen graphs.