New Spectral Results for Laplacian Harary Matrix and the HararyLaplacian-Energy-like Applying a Matrix Order Reduction
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2024
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In this paper, we introduce the concepts of Harary Laplacian-energy-like for a simple undirected and connected graph Gwith ordern. We also establish novel matrix results in this regard.Furthermore, by employing matrix order reduction techniques, we derive upper and lower bounds utilizing existing graph invariants and vertex connectivity. Finally, we characterize the graphs that achieve the aforementioned bounds by considering the generalized join operation of graphs.