Vladikavkazskij matematičeskij žurnal, Tome 16 (2014) no. 4, pp. 61-64
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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/
@article{VMJ_2014_16_4_a7,
author = {P. Siva Kota Reddy and K. M. Nagaraja and V. M. Siddalingaswamy},
title = {The edge $C_k$ graph of a~graph},
journal = {Vladikavkazskij matemati\v{c}eskij \v{z}urnal},
pages = {61--64},
year = {2014},
volume = {16},
number = {4},
language = {en},
url = {http://geodesic.mathdoc.fr/item/VMJ_2014_16_4_a7/}
}
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AU - P. Siva Kota Reddy
AU - K. M. Nagaraja
AU - V. M. Siddalingaswamy
TI - The edge $C_k$ graph of a graph
JO - Vladikavkazskij matematičeskij žurnal
PY - 2014
SP - 61
EP - 64
VL - 16
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UR - http://geodesic.mathdoc.fr/item/VMJ_2014_16_4_a7/
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%A K. M. Nagaraja
%A V. M. Siddalingaswamy
%T The edge $C_k$ graph of a graph
%J Vladikavkazskij matematičeskij žurnal
%D 2014
%P 61-64
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%G en
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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.
[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
[5] Prisner E., Graph Dyanamics, Longman, 1995 | MR
