- Six-star Graph, Even Felicitous Graph, Encoding
Abstract
In this work, we have identifified a way for encoding a secret message utilizing the GMJ (Graph Message Jumbled) Code and even felicitous labeling on fifive-star graphs K1,σ1 ∪ K1,σ2 ∪ K1,σ3 ∪ K1,σ4 ∪ K1,σ5 . For every star graph, we give two examples and use a Java program to apply alphabetical techniques to the Corona Number and Triangular Number. A strategy for labeling an even felicitous graph and flflowchart is provided for transforming plaintext into ciphertext (Picture Coding). Furthermore, we demonstrate an innovative application of these graph labeling techniques to epidemiological modeling through a detailed analysis of the SIR (Susceptible-Infected-Recovered) epidemic model on star networks. The paper shows how felicitous labeling can encode varying transmission probabilities and infection states, providing insights for targeted public health interventions. This interdisciplinary approach bridges cryptography, graph theory, and epidemiology, offffering both secure communication methods and practical disease spread modeling frameworks.