A Study on Minimal Doubly Resolving Sets of Certain Families of Networks

The suppression of harmful information and even its diffusion can be predicted and delayed by precisely finding sources with limited resources. The doubly resolving sets (DRSs) play a crucial role in determining where diffusion occurs in a network. Source detection problems are among the most challenging and exciting problems in complex networks. This problem has great significance in controlling any diffusion outbreak. The detection of a virus source in a network is basically locating a node that spreads the observed diffusion. This problem can be solved by using its connection to the well-known and well-studied minimal doubly resolving set (MDRS) problem, which reduces the number of observers needed to get an accurate answer. In this article, we investigate the MDRSs for the families of kayak paddle networks
$KP_{(r, s, t)}$
and lollipop networks
$L_{(r,s)}$
. It is concluded that the cardinality of MDRSs for
$KP_{(r, s, t)}$
is bounded, and it is unbounded for
$L_{(r,s)}$
.