Skolem Number of Subgraphs on the Triangular Lattice
Braxton Carrigan, Garrett Green · Communications on number theory and combinatorial theory. · 2021
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.