Abstract
In this paper, we study the spectral radius of graphs of order n with κ(G) ≤ k. We show that among those graphs, the maximal spectral radius is obtained uniquely at \({K_{n}^{k}}\), which is the graph obtained by joining k edges from k vertices of K n-1 to an isolated vertex. We also show that the spectral radius of \({K_{n}^{k}}\) will be very close to n − 2 for a fixed k and a sufficiently large n.
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Li, J., Shiu, W.C., Chan, W.H. et al. On the spectral radius of graphs with connectivity at most k . J Math Chem 46, 340–346 (2009). https://doi.org/10.1007/s10910-008-9465-5
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DOI: https://doi.org/10.1007/s10910-008-9465-5