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- W4387687223 abstract "Let $G$ be a simple connected graph and let $S_k(G)$ be the sum of the first $k$ largest signless Laplacian eigenvalues of $G$. It was conjectured by Ashraf, Omidi and Tayfeh-Rezaibe in 2013 that $S_k(G)leq e(G)+binom{k+1}{2}$ holds for $1leq kleq n-1$. They gave a proof for the conjecture when $k = 2$, but applied an incorrect key lemma. Therefore, the conjecture is still open when $k = 2$. In this paper, we prove that $S_2(G)<e(G)+3$ is true for any graphs which also confirm the conjecture when $k = 2$." @default.
- W4387687223 created "2023-10-17" @default.
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- W4387687223 date "2023-10-13" @default.
- W4387687223 modified "2023-10-18" @default.
- W4387687223 title "On the sum of the two largest signless Laplacian eigenvalues" @default.
- W4387687223 doi "https://doi.org/10.48550/arxiv.2310.08880" @default.
- W4387687223 hasPublicationYear "2023" @default.
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