## Eigenvalues of the Laplacian of a graph.(English)Zbl 0594.05046

From the authors’ abstract: ”Let G be a finite undirected graph with no loops or multiple edges. The Laplacian matrix $$\Delta$$ (G) of G is defined by $$\Delta_{ii}$$ $$=$$ the degree of vertex i, and $$\Delta_{ij}=-1$$ if there is an edge between vertex i and vertex j. In this paper the structure of the graph G is related to the eigenvalues of $$\Delta$$ (G). It is proved that all eigenvalues of $$\Delta$$ (G) are non- negative, do not exceed the number of vertices, and do not exceed twice the maximum vertex degree. The exact conditions for equalities are also given.”
Reviewer: A.Torgašev

### MSC:

 05C50 Graphs and linear algebra (matrices, eigenvalues, etc.)
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### References:

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