Skolem Number of Kagome Lattice Graphs

A proper Skolem labelling of a graph $G$ is a function assigning a positive integer to each vertex of $G$ such that any two vertices assigned the same integer are that distance apart in the graph. The Skolem number of a graph is smallest number $n$ such that there exists a proper Skolem labelling only using the positive integers less than or equal to $n$. In this paper, we will begin by proving the Skolem number for another family of subgraphs of the hexagonal lattice and then prove the Skolem number for two families of subgraphs of the Kagome Lattice.