Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Calculating a product of multiple graphs has been studied in mathematics, engineering, computer science, and more recently in network science, particularly in the context of multilayer networks. One of the important questions to be addressed in this area is how to characterize spectral properties of a product graph using those of its factor graphs. While several such characterizations have already been obtained analytically (mostly for adjacency spectra), characterization of Laplacian spectra of direct product and strong product graphs has remained an open problem. Here  develop practical methods to estimate Laplacian spectra of direct and strong product graphs from spectral properties of their factor graphs using a few heuristic assumptions. Numerical experiments shod that the proposed methods produced reasonable estimation with percentage errors confined within a ? 10 % range for most eigenvalues.
['Hiroki Sayama']
I am writing a research paper on a idea Estimation of Laplacian spectra of direct and strong product graphs
[{"from": "human", "value": "I am writing a research paper on a idea Estimation of Laplacian spectra of direct and strong product graphs"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Calculating a product of multiple graphs has been studied in mathematics, engineering, computer science, and more recently in network science, particularly in the context of multilayer networks. One of the important questions to be addressed in this area is how to characterize spectral properties of a product graph using those of its factor graphs. While several such characterizations have already been obtained analytically (mostly for adjacency spectra), characterization of Laplacian spectra of direct product and strong product graphs has remained an open problem. Here  develop practical methods to estimate Laplacian spectra of direct and strong product graphs from spectral properties of their factor graphs using a few heuristic assumptions. Numerical experiments shod that the proposed methods produced reasonable estimation with percentage errors confined within a ? 10 % range for most eigenvalues."}]