Eccentric completion of a graph

Document Type : Original paper

Authors

CHRIST (Deemed to be University), Bangalore

Abstract

The eccentric graph Ge of a graph G is a derived graph with the vertex set same as that of G and two vertices in Ge are adjacent if one of them is the eccentric vertex of the other. In this paper, the concepts of iterated eccentric graphs and eccentric completion of a graph are introduced and discussed.

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[1] J. Akiyama, K. Ando, and D. Avis, Eccentric graphs, Discrete Math. 56 (1985), no. 1, 1–6.
[2] F. Buckley and F. Harary, Distance in Graphs, Addison-Wesley, 1990.
[3] G. Chartrand, W. Gu, M. Schultz, and S.J. Winters, Eccentric graphs, Networks 34 (1999), no. 2, 115–121.
[4] P. Dankelmann, New bounds on proximity and remoteness in graphs, Commun. Comb. Optim. 1 (2016), no. 1, 29–41.
[5] J. Gimbert, M. Miller, F. Ruskey, and J. Ryan, Iterations of eccentric digraphs, Bull. Inst. Combin. Appl. 45 (2005), 41–50.
[6] J. T. Hedetniemi, S. T. Hedetniemi, R. C. Laskar, C. Renu, and H. M. Mulder, Different-distance sets in a graph, Commun. Comb. Optim. 4 (2019), no. 2, 151–171.
[7] J. V. Kureethara and M. Sebastian, Line completion number of grid graph  ppm , Commun. Comb. Optim. 6 (2021), no. 2, 299–313.
[8] E. Prisner, Graph Dynamics, vol. 338, CRC Press, 1995.
[9] D. B. West, Introduction to Graph Theory, vol. 2, Prentice hall of India, New Delhi, 2001.