Some Special Graceful Labeling Results of Pentagonal Pyramidal Graceful Graphs

ABSTRACT

Numbers of the form (𝑛^2 (𝑛+1))/2 for all n≥1 are called pentagonal pyramidal numbers. Let G be a graph with p vertices and q edges. Let Ψ : V(G) →{0, 1, 2… 𝑀𝑟} where 𝑀𝑟 is the 𝑟𝑡ℎ pentagonal pyramidal number be an injective function. Define the function Ψ*:E(G) →{1,6,18,.., 𝑀𝑟} such that Ψ *(uv) = |Ψ (u)- Ψ (v)| for all edges uvϵE(G). If Ψ*(E (G)) is a sequence of distinct consecutive pentagonal pyramidal numbers {𝑀1,𝑀2, …, 𝑀𝑟}, then the function Ψ is said to be pentagonal pyramidal graceful labeling and the graph which admits such a labeling is called a pentagonal pyramidal graceful graph. In this paper, some special graceful labeling results of pentagonal pyramidal graceful graphs is studied.