  We explore the networks that yield the largest mean consensus time of voter
models under different update rules. By analytical and numerical means, we show
that the so-called lollipop graph, barbell graph, and double star graph
maximise the mean consensus time under the update rules called the link
dynamics, voter model, and invasion process, respectively. For each update
rule, the largest mean consensus time scales as O(N^3), where N is the number
of nodes in the network.
