On the $g$-good-neighbor connectivity of graphs
Abstract
Connectivity and diagnosability are two important parameters for the fault tolerant of an interconnection network $G$. In 1996, Fàbrega and Fiol proposed the $g$-good-neighbor connectivity of $G$. In this paper, we show that $1\leq \kappa^g(G)\leq n-2g-2$ for $0\leq g\leq \left\{\Delta(G),\left\lfloor \frac{n-3}{2}\right\rfloor\right\}$, and graphs with $\kappa^g(G)=1,2$ and trees with $\kappa^g(T_n)=n-t$ for $4\leq t\leq \frac{n+2}{2}$ are characterized, respectively. In the end, we get the three extremal results for the $g$-good-neighbor connectivity.
- Publication:
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arXiv e-prints
- Pub Date:
- May 2019
- DOI:
- 10.48550/arXiv.1905.11254
- arXiv:
- arXiv:1905.11254
- Bibcode:
- 2019arXiv190511254W
- Keywords:
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- Mathematics - Combinatorics
- E-Print:
- 14 pages, 2 figures. arXiv admin note: substantial text overlap with arXiv:1904.06527