Geodesic
Minimum cuts of distance-regular digraphs
The electronic journal of combinatorics, Tome 24 (2017) no. 4

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Zbl
In this paper, we investigate the structure of minimum vertex and edge cuts of distance-regular digraphs. We show that each distance-regular digraph $\Gamma$, different from an undirected cycle, is super edge-connected, that is, any minimum edge cut of $\Gamma$ is the set of all edges going into (or coming out of) a single vertex. Moreover, we will show that except for undirected cycles, any distance regular-digraph $\Gamma$ with diameter $D=2$, degree $k\leq 3$ or $\lambda=0$ ($\lambda$ is the number of 2-paths from $u$ to $v$ for an edge $uv$ of $\Gamma$) is super vertex-connected, that is, any minimum vertex cut of $\Gamma$ is the set of all out-neighbors (or in-neighbors) of a single vertex in $\Gamma$. These results extend the same known results for the undirected case with quite different proofs.
DOI : 10.37236/6167
Classification : 05C20, 05C40
Mots-clés : distance-regular digraphs, strongly regular digraphs, minimum cuts, connectivity 
Saleh Ashkboos; Gholamreza Omidi; Fateme Shafiei; Khosro Tajbakhsh. Minimum cuts of distance-regular digraphs. The electronic journal of combinatorics, Tome 24 (2017) no. 4. doi: 10.37236/6167
@article{10_37236_6167,
     author = {Saleh Ashkboos and Gholamreza Omidi and Fateme Shafiei and Khosro Tajbakhsh},
     title = {Minimum cuts of distance-regular digraphs},
     journal = {The electronic journal of combinatorics},
     year = {2017},
     volume = {24},
     number = {4},
     doi = {10.37236/6167},
     zbl = {1372.05085},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/6167/}
}
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