Prime Graph and Its Structures

TL;DR

This paper explores the properties and internal structures of prime sum graphs, where vertices are connected if their sum is prime, providing insights into their fundamental characteristics and subgraph configurations.

Contribution

It introduces the basic properties of prime sum graphs and investigates specific induced subgraph structures within them, offering new structural insights.

Findings

Characterization of prime sum graph properties

Identification of specific induced subgraph structures

Insights into the internal organization of prime sum graphs

Abstract

We study the basic properties of a prime sum graph, which is a simple graph defined on $\mathbb N$ where two vertices are adjacent if and only if their sum is a prime number. Further, we investigate some specific structures that appear inside a prime sum graph as an induced subgraph.