Geodesic
Two-distance-primitive graphs
The electronic journal of combinatorics, Tome 27 (2020) no. 4
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A 2-distance-primitive graph is a vertex-transitive graph whose vertex stabilizer is primitive on both the first step and the second step neighborhoods. Let $\Gamma$ be such a graph. This paper shows that either $\Gamma$ is a cyclic graph, or $\Gamma$ is a complete bipartite graph, or $\Gamma$ has girth at most $4$ and the vertex stabilizer acts faithfully on both the first step and the second step neighborhoods. Also a complete classification is given of such graphs satisfying that the vertex stabilizer acts $2$-transitively on the second step neighborhood. Finally, we determine the unique 2-distance-primitive graph which is locally cyclic.
DOI : 10.37236/8890
Classification : 05C12, 05E18, 20B25
Mots-clés : locally cyclic graph, 2-distance-primitive graph 
@article{10_37236_8890,
     author = {Wei Jin and Ci Xuan Wu and Jin Xin Zhou},
     title = {Two-distance-primitive graphs},
     journal = {The electronic journal of combinatorics},
     year = {2020},
     volume = {27},
     number = {4},
     doi = {10.37236/8890},
     zbl = {1456.05045},
     url = {http://geodesic.mathdoc.fr/articles/10.37236/8890/}
}
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Wei Jin; Ci Xuan Wu; Jin Xin Zhou. Two-distance-primitive graphs. The electronic journal of combinatorics, Tome 27 (2020) no. 4. doi: 10.37236/8890

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