Comparison of Different Properties of Graph Using Adjacency Matrix and Signless Laplacian Matix

This study highlights the advantages of using the Signless Laplacian spectrum over the traditional Adjacency matrix spectrum for graph representation. It demonstrates that the Signless Laplacian possesses greater representational power and stronger characterization properties, making it a more effective tool for analyzing graph structures. Particularly, in the case of Sierpinski graphs, the eigenvalue analysis of the Signless Laplacian matrix outperforms that of the Adjacency matrix, reinforcing its utility in encoding and interpreting graph properties.