Geodesic
On Crown-Free Graphs with Regular $\mu$-Subgraphs, II
Matematičeskie zametki, Tome 74 (2003) no. 3, pp. 396-406 
V. V. Kabanov; A. A. Makhnev; D. V. Paduchikh. On Crown-Free Graphs with Regular $\mu$-Subgraphs, II. Matematičeskie zametki, Tome 74 (2003) no. 3, pp. 396-406. http://geodesic.mathdoc.fr/item/MZM_2003_74_3_a7/
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     title = {On {Crown-Free} {Graphs} with {Regular} $\mu${-Subgraphs,} {II}},
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Voir la notice de l'article provenant de la source Math-Net.Ru

The crown is the complete multipartite graph $K_{1,1,3}$. Terwilliger graphs without crowns and graphs without 3-cocliques with regular $\mu$-subgraphs of given positive degree are studied. As a corollary, the local structure of graphs in which the neighborhoods of vertices are regular Terwilliger graphs of diameter 2 and some of these neighborhoods contain no 7-paws is determined. Connected crown-free graphs in which $\mu$-subgraphs are edge regular graphs of diameter not exceeding 2 with given parameters are described.

[1] Numata M., “A characterization of Grassman and Johnson graphs”, J. Comb. Theory. Ser. B, 48 (1990), 178–190 | DOI | MR | Zbl

[2] Kabanov V. V., “O grafakh bez koron s regulyarnymi $\mu$-podgrafami”, Matem. zametki, 67:6 (2000), 874–881 | MR | Zbl

[3] Makhnev A. A., “Ob odnom klasse grafov bez 3-lap”, Matem. zametki, 63:3 (1998), 407–413 | MR | Zbl

[4] Kabanov V. V., Makhnev A. A., “Grafy bez 3-lap s ravnomoschnymi $\mu$-podgrafami”, Izv. Ural. gos. un-ta. Matem., mekh., 1998, no. 10, 44–68 | MR | Zbl

[5] Brouwer A. E., Cohen A. M., Neumaier A., Distance-Regular Graphs, Springer-Verlag, 1989

[6] Cameron P., Van Lint J., Designs, Graphs, Codes and their Links, London Math. Soc. Student Texts, 22, Cambr. Univ. Press, Cambridge, 1981