| Autor: |
Conde, Cristian, Dratman, Ezequiel, Grippo, Luciano N. |
| Rok vydání: |
2019 |
| Předmět: |
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| Druh dokumentu: |
Working Paper |
| Popis: |
The edge-connectivity of a graph is the minimum number of edges whose deletion disconnects the graph. Let $\Delta(G)$ the maximum degree of a graph $G$ and let $\rho(G)$ be the spectral radius of $G$. In this article we present a lower bound for $\Delta(G)-\rho(G)$ in terms of the edge connectivity of $G$, where $G$ is a nonregular distance-hereditary graph. We also prove that $\rho(G)$ reaches the maximum at a unique graph in $\mathcal G$, when $\vert V(G)\vert = n$, and $\mathcal G$ either is in the class of graphs with bounded tree-width or is in the class of block graphs with prescribed independence number. |
| Databáze: |
arXiv |
| Externí odkaz: |
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