id: 06034526
dt: j
an: 06034526
au: Zhai, Mingqing; Lin, Huiqiu; Wang, Bing
ti: Sharp upper bounds on the second largest eigenvalues of connected graphs.
so: Linear Algebra Appl. 437, No. 1, 236-241 (2012).
py: 2012
pu: Elsevier Science Inc. (North-Holland), New York, NY
la: EN
cc: 
ut: bipartite graph; the second largest eigenvalue
ci: Zbl 0666.05056
li: doi:10.1016/j.laa.2012.02.004
ab: Summary: Let $λ_{2}$ be the second largest eigenvalue of a graph. {\it D.
    I. Powers} [Linear Algebra Appl. 101, 121‒133 (1988; Zbl 0666.05056)]
    gave some upper bounds of $λ_{2}$ for general graphs and bipartite
    graphs, respectively. Considering that these bounds are not always
    attainable for connected graphs, we present sharp upper bounds of
    $λ_{2}$ for connected graphs and connected bipartite graphs in this
    paper. Moreover, the extremal graphs are completely characterized.
rv: