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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

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.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

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.

References

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