Minimizing the least eigenvalue of unicyclic graphs with fixed diameter. (English) Zbl 1216.05081
Summary: Let \(\mathcal U(n,d)\) be the set of unicyclic graphs on \(n\) vertices with diameter \(d\). In this article, we determine the unique graph with minimal least eigenvalue among all graphs in \(\mathcal U(n,d)\). It is found that the extremal graph is different from that for the corresponding problem on maximal eigenvalue as done by H.Q. Liu, M. Lu and F. Tian[On the spectral radius of unicyclic graphs with fixed diameter, Linear Algebra Appl. 420, No. 2–3, 449–457 (2007; Zbl 1108.05063)].
Citations:
Zbl 1108.05063References:
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