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On Eccentric Digraphs of Graphs

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DOI: 10.4236/am.2011.26093    4,730 Downloads   9,260 Views   Citations


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.

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The authors declare no conflicts of interest.

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M. 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.


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