Geodesic
On Crown-Free Graphs with Regular $\mu$-Subgraphs, II
Matematičeskie zametki, Tome 74 (2003) no. 3, pp. 396-406.

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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. 
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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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