The edge \(C_K\) graph of a graph

Siva Kota Reddy P. , Nagaraja K. M. , Siddalingaswamy V. M.
Vladikavkaz Mathematical Journal 2014. Vol. 16. Issue 4.

Abstract:
For any integer \(k \geq 4\), 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.

Keywords: edge \(C_k\) graph, triangular line graph, line graph, convergent, periodic, mortal, transition number

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