On the sum of the first two largest signless Laplacian eigenvalues of a graph

Zi-Ming Zhou, Chang-Xiang He, Hai-Ying Shan

For a graph $G$, let $S_2(G)$ be the sum of the first two largest signless Laplacian eigenvalues of $G$, and $f(G)=e(G)+3-S_2(G)$. Oliveira, Lima, Rama and Carvalho conjectured tha…