| Abstrakt: |
Abstract: Let µ_{n-1}(G) be the algebraic connectivity, and let µ_{1}(G) be the Laplacian spectral radius of a k-connected graph G with n vertices and m edges. In this paper, we prove that {\mu _{n - 1}}(G) \geqslant \frac{{2n{k^2}}}{{(n(n - 1) - 2m)(n + k - 2) + 2{k^2}}} , with equality if and only if G is the complete graph Kn or Kn − e. Moreover, if G is non-regular, then {\mu _1}(G) < 2\Delta - \frac{{2(n\Delta - 2m){k^2}}}{{2(n\Delta - 2m)({n^2} - 2n + 2k) + n{k^2}}} , where ▵ stands for the maximum degree of G. Remark that in some cases, these two inequalities improve some previously known results. |
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