On Laplacian and Distance Laplacian Spectra of Generalized Fan Graph & a New Graph Class
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| Format: | Preprint |
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2024
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| _version_ | 1866912912209084416 |
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| author | Banerjee, Subarsha Ganguly, Soumya |
| author_facet | Banerjee, Subarsha Ganguly, Soumya |
| contents | 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 $\mathcal{NC}(F_{m,n})$. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2412_19095 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On Laplacian and Distance Laplacian Spectra of Generalized Fan Graph & a New Graph Class Banerjee, Subarsha Ganguly, Soumya Combinatorics 05C07, 05C12, 05C50 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 $\mathcal{NC}(F_{m,n})$. |
| title | On Laplacian and Distance Laplacian Spectra of Generalized Fan Graph & a New Graph Class |
| topic | Combinatorics 05C07, 05C12, 05C50 |
| url | https://arxiv.org/abs/2412.19095 |