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arXiv · 2603.07232

On distance integral and distance Laplacian integral graphs

S. Pirzada·Ummer Mushtaq·Leonardo de Lima
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Abstract

Let $G$ be a connected graph on $n$ vertices and let $D(G)$ and $D^{L}(G)$ be the distance and the distance Laplacian matrices associated with $G$. A graph $G$ is said to be $D$-integral (resp. $D^L$-integral) if all eigenvalues of $D(G)$ (resp. $D^L(G)$) are integers. In this paper, we obtain various conditions under which the graphs $a\overline{K_m}\nabla C_n$ and $K_{p,p}\nabla C_n$ are distance integral. We also obtain conditions on $m$, $n$ under which the dumbbell graph $\boldsymbol{DB}(W_{m,n})$ is $D^L$-integral.

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S. Pirzada, Ummer Mushtaq, Leonardo de Lima. 2026-03-07. On distance integral and distance Laplacian integral graphs. https://arxiv.org/abs/2603.07232

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