Labeling On Pentagonal Pyramidal Graceful Graph

Numbers that can be expressed as (r ^{2} (r+1)) /2 for
all r ≥ 1 are called pentagonal pyramidal numbers. Assume G to be a
graph with p vertices and q edges. Let Φ: V(G) →{0, 1, 2… B
_{c}} where B _{c} is the c
^{ℎ} number with a pentagonal pyramid, be an injective
function. Define the function Φ* :E(G) →{1,6,18,.., B _{c}
} such that Φ * (ab) = |Φ(a)- Φ(b)| which is true for
each and every edge abϵE(G). If Φ*(E(G)) represents a sequential
arrangement of non-identical successive pentagonal pyramidal numbers {B
_{1}, B _{2}, …, B _{c}},
then Φ can be regarded as the pentagonal pyramidal graceful labeling.
The graph permitting labeling of such kind can be referred to as a
pentagonal pyramidal graceful graph. This study examines some unique
pentagonal pyramidal elegant graph labeling outcomes.