Abstract
The crown is the complete multipartite graph K1,1,3. Terwilliger graphs without crowns and graphs without 3-cocliques with regular μ-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 μ-subgraphs are edge regular graphs of diameter not exceeding 2 with given parameters are described.
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