Siva Kota Reddy, P.; Nagaraja, K. M.; Siddalingaswamy, V. M. The edge \(C_k\) graph of a graph. (English) Zbl 1420.05153 Vladikavkaz. Mat. Zh. 16, No. 4, 61-64 (2014). 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 Keywords:edge \(C_k\) graph; triangular line graph; line graph; convergence; periodicity; mortality; transition number PDFBibTeX XMLCite \textit{P. Siva Kota Reddy} et al., Vladikavkaz. Mat. Zh. 16, No. 4, 61--64 (2014; Zbl 1420.05153) Full Text: MNR References: [1] Beineke L. W., “Characterizations of derived graphs”, J. Combinatorial Theory, 9 (1970), 129-135 · Zbl 0202.55702 · doi:10.1016/S0021-9800(70)80019-9 [2] Jarrett E. B., Transformations of graphs and digraphs, Ph. D. Thesis, Western Michigan University, 1991 [3] Harary F., Graph Theory, Addison-Wesley Publ. Co., 1969 · Zbl 0182.57702 [4] Menon Manju K., Vijayakumar A., “The edge \(C_4\) graph of a graph”, Ramanujan Math. Soc. Proc. of ICDM (Bangalore, India, December 15-18, 2006), Lecture Notes Series, 7, 2008, 245-248 · Zbl 1202.05116 [5] Prisner E., Graph Dyanamics, Longman, 1995 · Zbl 0848.05001 [6] Ore O., Theory of Graphs, Amer. Math. Soc. Colloq. Publ., 38, Amer. Math. Soc., Providence, RI, 1962 · Zbl 0105.35401 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.