Pell Labeling in Special Graph Classes: An Exploration of Cycles, Stars, and Related Structures

In a graph, define Pell labeling is a map: () → 0, 1, ⋯, -1 with an induced function *: () → defined by * () = () + 2 () for every ∈ () are all distinct where, ≤ 0. In addition to this a graph which admits Pell labeling concept is known as Pell graph. In this paper, the Pell labeling concepts applied for the following graphs such as splitting of Star, cycle with parallel chords, alternate double triangular Snake, ladder, Triangular ladder, diagonal ladder, shadow and splitting of path, bistar, subdivision of bistar, prism, , 2 and friendship graphs are studied. Our analysis contributes to the understanding of Pell labeling across a broad spectrum of graph configurations, highlighting its applicability and the unique characteristics of each considered graph family.