This paper focuses on the Pell graphs. We begin by explaining the basic terminology from the field of graph theory and highlighting some of the more important classes of graphs. We describe several Pell graph properties with additional explanations. In Chapter 3 we talk about properties which are directly linked to the definition of neighbours in Pell graphs (bipartiteness, coloring, matching). We introduce the canonical decomposition as an example of recursive decomposition. In Chapter 4 we describe properties based on distances between vertices (radius, diameter, center, periphery). In Chapter 5 we connect Pell graphs to Fibonacci cubes and in Chapter 6 to hypercubes. In the last two chapters we give a possible explanation for a numerical identity, linked to the Fibonacci numbers, and a visual representation of the graph Π_5.
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