## The edge $$C_k$$ graph of a graph.(English)Zbl 1420.05153

Summary: 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. Moreover, the dynamical behavior such as convergence, periodicity, mortality and touching number of $$E_k(G)$$ are studied.

### MSC:

 05C76 Graph operations (line graphs, products, etc.) 05C75 Structural characterization of families of graphs
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### References:

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