Optimized Modular Multiplicative Divisor Labeling for Efficient Minimum Spanning Tree Computation in Jellyfish Graphs Using Prims Algorithm
P. Kalarani, R. Revathi, R. Vijaykrishnaraj, A. Suganya, K. Vijayalakshmi · 2025
The Minimum Spanning Tree (MST) of the Jellyfish graph, which admits Modular Multiplicative Divisor (MMD) labeling, is analyzed using Prim's Algorithm. The Jellyfish graph extends a cycle$\boldsymbol{C}_{\mathbf{4}}$with pendant paths, resembling a jellyfish. Modular Multiplicative Divisor labeling assigns unique natural numbers to vertices, with edge labels derived modulo$\boldsymbol{n}$. Prim's algorithm efficiently computes the MST by selecting the lowest weight edges while ensuring connectivity, acyclicity, and minimal total weight. The study explores$\boldsymbol{J}(\boldsymbol{\theta},\boldsymbol{\omega})$graphs with even tentacles, highlighting the role of Modular Multiplicative Divisor labeling in optimizing spanning tree structures for network applications.