Comparison of Different Properties of Graph Using Adjacency Matrix and Signless Laplacian Matix
DOI:
https://doi.org/10.32628/IJSRSET25122211Keywords:
Signless Laplacian Spectrum, Adjacency Matrix, Graph Representation, Spectral Graph Theory, Eigenvalue Analysis, Graph CharacterizationAbstract
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.
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Mehta, H., S., and Acharya, U., P. [2017]: “Adjacency matrix of product of graphs”, Kalpa Publications in Computing, Vol. 2, pp. 158–165.
Merris, R. [1994]: “Laplacian matrices of graphs: A survey”, Linear Algebra and its Applications, Vol. 197–198, pp. 143-176.
MIRCHEV, M. J. [2015]: “APPLICATIONS OF SPECTRAL GRAPH THEORY IN THE FIELD OF TELECOMMUNICATIONS”, 23RD TELECOM 2015, SOFIA, BULGARIA.
Mohammed, A., M. [2017]: “Mixed graph representation and mixed graph isomorphism”, Gazi University Journal of Science, Vol. 30, Issue 1, pp. 303-310.
Mukherjee, C., and Mukherjee, G. [2014]: “Role of adjacency matrix in graph theory”, IOSR Journal of Computer Engineering, Vol. 16, Issue 2, Ver. III, pp. 58-63.
Muneshwar, R., A., and Bondar, K., L. [2014]: “On graph of a finite group”, IOSR Journal of Mathematics, Vol. 10, Issue 5, Ver. VI, pp. 05-09.
Narsingh Deo [2005]: “Graph Theory with applications to engineering and computer science”, Eastern Economy Edition, Prentice -Hall Of India Private Limited.
Nawaz, M. S., and Awan, M. F. [2013]: “Graph coloring algorithm using adjacency matrices”, International Journal of Scientific & Engineering Research, Vol. 4, Issue 4, pp. 1840-1842.
NEWMAN, M., W. [2000]: “THE LAPLACIAN SPECTRUM OF GRAPHS”, THESIS, HTTPS://WWW.SEAS.UPENN.EDU/~JADBABAI/ESE680/LAPLACIAN_THESIS.PDF
Pathak, R., and Kalita, B. [2012]: “Properties of some Euler graphs constructed from Euler diagram”, International Journal of Applied Sciences and Engineering Research, Vol. 1, No. 2, pp. 232-237.
Pieterse, V., and Black, P. [2008]: “Directed graph”, Dictionary of Algorithms and Data Structures.
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