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### Degree powers in graphs with a forbidden even cycle.

The Electronic Journal of Combinatorics [electronic only]

### Revisiting two classical results on graph spectra.

The Electronic Journal of Combinatorics [electronic only]

### Linear combinations of graph eigenvalues.

ELA. The Electronic Journal of Linear Algebra [electronic only]

### Spectral saturation: inverting the spectral Turán theorem.

The Electronic Journal of Combinatorics [electronic only]

### The spectral radius of subgraphs of regular graphs.

The Electronic Journal of Combinatorics [electronic only]

### Graphs with many copies of a given subgraph.

The Electronic Journal of Combinatorics [electronic only]

### Degree powers in graphs with forbidden subgraphs.

The Electronic Journal of Combinatorics [electronic only]

### Spectral radius and Hamiltonicity of graphs with large minimum degree

Czechoslovak Mathematical Journal

Let $G$ be a graph of order $n$ and $\lambda \left(G\right)$ the spectral radius of its adjacency matrix. We extend some recent results on sufficient conditions for Hamiltonian paths and cycles in $G$. One of the main results of the paper is the following theorem: Let $k\ge 2,$ $n\ge {k}^{3}+k+4,$ and let $G$ be a graph of order $n$, with minimum degree $\delta \left(G\right)\ge k.$ If $\lambda \left(G\right)\ge n-k-1,$ then $G$ has a Hamiltonian cycle, unless $G={K}_{1}\vee \left({K}_{n-k-1}+{K}_{k}\right)$ or $G={K}_{k}\vee \left({K}_{n-2k}+{\overline{K}}_{k}\right).$

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