CHARACTERIZATION OF THE INDUCED SUM AND MOD SUM GRAPHS

Abstract

The idea of sum graphs, first introduced by Harary in 1990, has since sparked numerous investigations into their classification and determination of sum numbers across diverse graph classes. Recognizing the connectivity constraints of non-trivial sum graphs, Boland et al., extended this concept to mod sum graphs in the same year. In contrast to existing approaches, our study focuses on characterizing the induced sum graphs and mod sum graphs for sets with arithmetic significance, such as arithmetic progression, Fibonacci numbers and prime numbers. By examining the patterns and relationship within these graphs, we can gain a deeper understanding of the underlying structure and properties of the sets or sequences under consideration. This understanding can lead to insight into various mathematical phenomena, aid in problem-solving, and inform the development of mathematical theories and applications.