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arXiv · 2412.19095

On Laplacian and Distance Laplacian Spectra of Generalized Fan Graph & a New Graph Class

Subarsha Banerjee·Soumya Ganguly
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Abstract

Given a graph $G$, the Laplacian matrix of $G$, $L(G)$ is the difference of the adjacency matrix $A(G)$ and $\text{Deg}(G)$, where $\text{Deg}(G)$ is the diagonal matrix of vertex degrees. The distance Laplacian matrix $D^L({G})$ is the difference of the transmission matrix of $G$ and the distance matrix of $G$. In the given paper, we first obtain the Laplacian and distance Laplacian spectrum of generalized fan graphs. We then introduce a new graph class which is denoted by $\mathcal{NC}(F_{m,n})$. Finally, we determine the Laplacian spectrum and the distance Laplacian spectrum of $\mathcal{NC}(F_{m,n})$.

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Subarsha Banerjee, Soumya Ganguly. 2024-12-26. On Laplacian and Distance Laplacian Spectra of Generalized Fan Graph & a New Graph Class. https://doi.org/10.2478/ijmce-2025-0021

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