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- W2943556103 abstract "Let $G$ be a graph of order $n$, and let $q_1(G)geq q_2(G)geqcdotsgeq q_n(G)$ denote the signless Laplacian eigenvalues of $G$. Ashraf and Tayfeh-Rezaie [Electron. J. Combin. 21 (3) (2014) #P3.6] showed that $q_1(G)+q_1(overline{G})leq 3n-4$, with equality holding if and only if $G$ or $overline{G}$ is the star $K_{1,n-1}$. In this paper, we discuss the following problem: for $ngeq6$, does $q_2(G)+q_2(overline{G})leq 2n-5$ always hold? We provide positive answers to this problem for the graphs with disconnected complements and the bipartite graphs, and determine the graphs attaining the bound. Moreover, we show that $q_2(G)+q_2(overline{G})geq n-2$, and the extremal graphs are also characterized." @default.
- W2943556103 created "2019-05-09" @default.
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- W2943556103 date "2019-04-30" @default.
- W2943556103 modified "2023-09-26" @default.
- W2943556103 title "Signless Laplacian eigenvalue problems of Nordhaus-Gaddum type" @default.
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- W2943556103 doi "https://doi.org/10.48550/arxiv.1904.13225" @default.
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