Modular Multiplicative Graphs

Abstract

In this paper, a new type of labeled graphs, called modular multiplicative graphs, is introduced and studied. Specifically, we show that every graph is a subgraph of a modular multiplicative graph. Later, we introduce \(k\)-modular multiplicative graphs and prove that certain families of paths and cycles admit such a label. We conclude with several open problems and areas of future possible research, including a note on harmonious graph labels.