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- W2999046549 abstract "Let $muleft( Gright) $ and $mu_{min}left( Gright) $ be the largest and smallest eigenvalues of the adjacency matrix of a graph $G$. Our main results are: (i) If $H$ is a proper subgraph of a connected graph $G$ of order $n$ and diameter $D$, then $$ muleft( Gright) -muleft( Hright) >{1overmuleft( Gright) ^{2D}n}. $$ (ii) If $G$ is a connected nonbipartite graph of order $n$ and diameter $D$, then $$ muleft( Gright) +mu_{min}left( Gright) >{2overmuleft( Gright) ^{2D}n}. $$ For large $mu $ and $D$ these bounds are close to the best possible ones." @default.
- W2999046549 created "2020-01-23" @default.
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- W2999046549 date "2007-01-17" @default.
- W2999046549 modified "2023-09-26" @default.
- W2999046549 title "Revisiting Two Classical Results on Graph Spectra" @default.
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- W2999046549 doi "https://doi.org/10.37236/932" @default.
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