Abstract
Let $G$ be a connected graph and $D^{L}(G) = \operatorname{Tr}(G) - D(G)$ be the distance Laplacian matrix of $G$, where $\operatorname{Tr}(G)$ and $D(G)$ are diagonal matrix with vertex transmissions of $G$ and distance matrix of $G$, respectively. The $D^{L}$-spectral radius of $G$ is defined as the largest absolute value of the distance Laplacian eigenvalues of $G$. In this paper, we characterize the unique extremal graphs which maximize the $D^{L}$-spectral radius among the complements of trees and unicyclic graphs, respectively.
Funding Statement
The research is supported by NSFC (Nos. 12361071 and 11901498), the Scientific Research Plan of Universities in Xinjiang, China (No. XJEDU2021I001), XJTCDP (No. 04231200746), BS (No. 62031224601).
Citation
Kang Liu. Dan Li. Yuanyuan Chen. "Distance Laplacian Spectral Radius of the Complements of Trees and Unicyclic Graphs." Taiwanese J. Math. 28 (1) 1 - 15, February, 2024. https://doi.org/10.11650/tjm/231002
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