Algebraic connectivity of Kronecker products of line graphs
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866915108218732544 |
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| author | Chauhan, Shivani Reddy, A. Satyanarayana |
| author_facet | Chauhan, Shivani Reddy, A. Satyanarayana |
| contents | Let $X$ be a tree with $n$ vertices and $L(X)$ be its line graph. In this work, we completely characterize the trees for which the algebraic connectivity of $L(X)\times K_m$ is equal to $m-1$, where $\times$ denotes the Kronecker product. We provide a few necessary and sufficient conditions for $L(X)\times K_m$ to be Laplacian integral. The algebraic connectivity of $L(X)\times K_m$, where $X$ is a tree of diameter $4$ and $k$-book graph is discussed. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_06040 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Algebraic connectivity of Kronecker products of line graphs Chauhan, Shivani Reddy, A. Satyanarayana Combinatorics 05C05, 05C76 Let $X$ be a tree with $n$ vertices and $L(X)$ be its line graph. In this work, we completely characterize the trees for which the algebraic connectivity of $L(X)\times K_m$ is equal to $m-1$, where $\times$ denotes the Kronecker product. We provide a few necessary and sufficient conditions for $L(X)\times K_m$ to be Laplacian integral. The algebraic connectivity of $L(X)\times K_m$, where $X$ is a tree of diameter $4$ and $k$-book graph is discussed. |
| title | Algebraic connectivity of Kronecker products of line graphs |
| topic | Combinatorics 05C05, 05C76 |
| url | https://arxiv.org/abs/2308.06040 |