Geodesic
New edge neighborhood graphs
Czechoslovak Mathematical Journal, Tome 47 (1997) no. 3, pp. 501-504 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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 $\mathcal N_e$.
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 $\mathcal N_e$.
Classification : 05C75 
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     author = {Ali, Ali A. and Alsardary, Salar Y.},
     title = {New edge neighborhood graphs},
     journal = {Czechoslovak Mathematical Journal},
     pages = {501--504},
     year = {1997},
     volume = {47},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_1997_47_3_a9/}
}
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Ali, Ali A.; Alsardary, Salar Y. New edge neighborhood graphs. Czechoslovak Mathematical Journal, Tome 47 (1997) no. 3, pp. 501-504. http://geodesic.mathdoc.fr/item/CMJ_1997_47_3_a9/

[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 | Zbl

[3] B. Zelinka: Edge neighborhood graphs. Czech. Math. J. 36(111) (1986), 44–47. | MR