New edge neighborhood graphs

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Let G be an undirected simple connected graph, and e = uv be an edge of G. Let NG(e) be the subgraph of G induced by the set of all vertices of G which are not incident to e but are adjacent to u or v. Let Ne be the class of all graphs H such that, for some graph G, NG (e) ≅ H for every edge e of G. Zelinka [3] studied edge neighborhood graphs and obtained some special graphs in Ne. Balasubramanian and Alsardary [1] obtained some other graphs in Ne. In this paper we given some new graphs in Ne.

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