A Skolem sequence can be thought of as a labelled path where any two vertices with the same label are that distance apart. This concept has naturally been generalized to graph labelling. This brings rise to the question; “what is the smallest set of consecutive positive integers we can use to properly Skolem label a graph?” This is known as the Skolem number of the graph. In this paper we give the Skolem number for three natural vertex induced subgraphs of the triangular lattice graph.
Carrigan, Braxton and Green, Garrett
"Skolem Number of Subgraphs on the Triangular Lattice,"
Communications on Number Theory and Combinatorial Theory: Vol. 2
, Article 2.
Available at: https://research.library.kutztown.edu/contact/vol2/iss1/2