For an integer Formula: see text, consider a collection of numbers Formula: see text and a network Formula: see text with Formula: see text and Formula: see text. The challenge is to create a variety of network designs that allow each edge in the network to employ a single number from the set Formula: see text to each edge in the network, ensuring that the amount of accumulation charges at each nodes (connection points) must differ. An edge Formula: see text graceful labeling (EFormula: see textGL) of a network Formula: see text defined as a bijection Formula: see text from the edge set Formula: see text to the numbers Formula: see text such that the derived transformation Formula: see text, given by: Formula: see text, where Formula: see text, is an injective. Nine designs for wheel-related planar networks and three designs for non-planar networks are presented in this paper. Every one of these networks satisfies our requirements for features and specifications.
Deen et al. (Fri,) studied this question.