Geodesic
The edge $C_k$ graph of a~graph
Vladikavkazskij matematičeskij žurnal, Tome 16 (2014) no. 4, pp. 61-64

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For any integer $k\geq4$, the edge $C_k$ graph $E_k(G)$ of a graph $G=(V,E)$ has all edges of $G$ as it vertices, two vertices in $E_k(G)$ are adjacent if their corresponding edges in $G$ are either incident or belongs to a copy of $C_k$. In this paper, we obtained the characterizations for the edge $C_k$ graph of a graph $G$ to be connected, complete, bipartite etc. It is also proved that the edge $C_4$ graph has no forbidden subgraph characterization. Mereover, the dynamical behavior such as convergence, periodicity, mortality and touching number of $E_k(G)$ are studied. 
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     title = {The edge $C_k$ graph of a~graph},
     journal = {Vladikavkazskij matemati\v{c}eskij \v{z}urnal},
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     publisher = {mathdoc},
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P. Siva Kota Reddy; K. M. Nagaraja; V. M. Siddalingaswamy. The edge $C_k$ graph of a~graph. Vladikavkazskij matematičeskij žurnal, Tome 16 (2014) no. 4, pp. 61-64. http://geodesic.mathdoc.fr/item/VMJ_2014_16_4_a7/