Generation of Specialized Graph Classes Using Hyper-edge Replacement P System

Graphs serve as flexible representations for capturing relationships between entities, while graph grammar offers a rule-based framework for transforming and generating graphs. In recent years, hyper-edge replacement graph grammar has emerged as a significant tool for generating both graphs and hypergraphs. George Paun introduced membrane computing, also known as the P system, as a computational paradigm that draws inspiration from biological systems. The intricate processes observed at the cellular level initially inspired the development of membrane computing. In this study, we leverage the ability of the hyper-edge replacement graph rewriting P system to generate new graphs using minimal-order hyper-edge rules, resulting in a large collection of graphs. Our primary objective is to produce cycle, tree, wheel, and broom graphs, as well as graphs that demonstrate resemblances to cycle, tree, and wheel graphs. This entails the generation of a multitude of graph types, including pan, prism, sunlet, tadpole, web, binary, ternary, k-ary trees, gear, helm, flower, and sunflower. © (2024), (International Association of Engineers). All rights reserved.