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Summary:
Let $G$ be an undirected simple connected graph, and $e=uv$ be an edge of $G$. Let $N_G(e)$ 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 $\mathcal N_e$ be the class of all graphs $H$ such that, for some graph $G$, $N_G(e)\cong H$ for every edge $e$ of $G$. Zelinka [3] studied edge neighborhood graphs and obtained some special graphs in $\mathcal N_e$. Balasubramanian and Alsardary [1] obtained some other graphs in $\mathcal N_e$. In this paper we given some new graphs in $\mathcal N_e$.
References:
[1] K. Balasubramanian, Salar Y. Alsardary: On edge neighborhood graphs (Communicated, Dirasat J. of Science).
[2] F. Harary: Graph Theory. Addison Wesley, Reading, Mass., 1969. MR 0256911 | Zbl 0196.27202
[3] B. Zelinka: Edge neighborhood graphs. Czech. Math. J. 36(111) (1986), 44–47. MR 0822865
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