The Q-index and connectivity of graphs
Abstract
A connected graph $G$ is said to be $k$-connected if it has more than $k$ vertices and remains connected whenever fewer than $k$ vertices are deleted. In this paper, for a connected graph $G$ with sufficiently large order, we present a tight sufficient condition for $G$ with fixed minimum degree to be $k$-connected based on the $Q$-index. Our result can be viewed as a spectral counterpart of the corresponding Dirac type condition.
- Publication:
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arXiv e-prints
- Pub Date:
- September 2021
- DOI:
- 10.48550/arXiv.2109.07656
- arXiv:
- arXiv:2109.07656
- Bibcode:
- 2021arXiv210907656Z
- Keywords:
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- Mathematics - Combinatorics;
- 05C50
- E-Print:
- 11 pages. arXiv admin note: text overlap with arXiv:2109.07347