A review on graceful and sequential integer additive set-labeled graphs

Abstract

Let be the set of all non-negative integers and be its power set. Then, an integer additive set-labeling (IASL) of a graph G is an injective function , such that the induced function defined by and an integer additive set-indexer (IASI) is an integer additive set-labeling such that the induced function is also injective. An integer additive set-labeling (or an integer additive set-indexer) is said to be a graceful integer additive set-labeling (or graceful integer additive set-indexer) if and an integer additive set-labeling (or an integer additive set-indexer) is said to be a sequential integer additive set-labeling (or sequential integer additive set-indexer) if . In this write-up, we creatively and critically review certain studies made on graceful integer additive set-labeling and sequential integer additive set-labeling of given graphs and certain properties and characteristics of the graphs which satisfy this type of set-labelings.