We say that a blinking node system modulo $n$ is an ordered pair $(G,L)$ where $G$ is a graph and $L$ is an on-labelling which indicates when vertices can be visited. An On-Hamiltonian walk is a sequence of all the vertices of $G$ such that the position of each vertex modulo $n$ is an integer of the label of that vertex. This paper will primarily investigate finding the shortest On-Hamiltonian walks in a blinking node system on complete graphs and complete bipartite graphs but also establishes the terminology and initial observations for working with blinking node systems on other graphs.
Carrigan, Braxton and Hammer, James
"Traveling in Networks with Blinking Nodes,"
Theory and Applications of Graphs: Vol. 5
, Article 2.
Available at: https://digitalcommons.georgiasouthern.edu/tag/vol5/iss1/2