ABSTRACT The eccentricity e(u) of a vertex u is the maximum distance of u to any other vertex of G. A vertex v is an eccentric vertex of vertex u if the distance from u to v is equal to e(u). The eccentric digraph ED(G) of a graph (digraph) G is the digraph that has the same vertex as G and an arc from u to v exists in ED(G) if and only if v is an eccentric vertex of u in G. In this paper, we have considered an open problem. Partly we have characterized graphs with specified maximum degree such that ED(G) = G.
Cite this paper
nullM. Huilgol, S. Asif Ulla S. and S. A. R., "On Eccentric Digraphs of Graphs," Applied Mathematics, Vol. 2 No. 6, 2011, pp. 705-710. doi: 10.4236/am.2011.26093.
 M. I. Huilgol, S. A. S. Ulla and A. R. Sunilchandra, “On Eccentric Digraphs of Graphs,” Proceedings of the In-ternational Conference on Emerging Trends in Mathe-matics and Computer Applications, MEPCO Schlenk En-gineering College, Sivakasi, 16-18 December 2010, pp. 41-44.
 F. Buckley and F. Harary, “Distance in Graphs,” Addison-Wesley, Redwood City, 1990.
 G. Chartrand and L. Lesniak, “Graphs and Digraphs,” 3rd Edition, Chapman & Hall, London, 1996.
 F. Buckley, “The Eccentric Digraph of a Graph,” Congressus Numerantium, Vol. 149, 2001, pp. 65-76.
 G. Johns and K. Sleno, “Antipodal Graphs and Digraphs,” International Journal of Mathematics and Mathematical Sciences, Vol. 16, No. 3, 1993, pp. 579-586.
 R. Aravamudhan and B. Rajendran, “On Antipodal Graphs,” Discrete Mathematics, Vol. 49, No. 1, 1984, pp. 193-195. doi:10.1016/0012-365X(84)90117-1
 J. Akiyama, K. Ando and D. Avis, “Eccentric Graphs,” Discrete Mathematics, Vol. 56, No. 1, 1985, pp. 1-6.
 J. Boland and M. Miller, “The Eccentric Digraph of a Digraph,” Proceedings of the 12th Australasian Workshop of Combinatorial Algorithms (AWOCA 2001), Freiburg, 3-7 September 2001, pp. 66-70.
 J. Gimbert, M. Miller, F. Ruskey and J. Ryan, “Iterations of Eccentric Digraphs,” Bulletin of the Institute of Combinatorics and Its Applications, Vol. 45, 2005, pp. 41-50.
 J. Boland, F. Buckley and M. Miller, “Eccentric Digraphs,” Discrete Mathematics, Vol. 286, No. 1-2, 2004, pp. 25-29. doi:10.1016/j.disc.2003.11.041
 R. Nandakumar and K. R. Pathasarathy, “Unique Eccentric Point Graphs,” Discrete Mathematics, Vol. 46, No. 1, 1983, pp. 69-74. doi:10.1016/0012-365X(83)90271-6