On Eccentric Digraphs of Graphs

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.

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.

Keywords

Eccentric Vertex, Eccentric Degree, Eccentric Digraph, Degree Sequence, Eccentric Degree Sequence

Eccentric Vertex, Eccentric Degree, Eccentric Digraph, Degree Sequence, Eccentric Degree Sequence

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.

nullM. Huilgol, S. Asif Ulla S. and S. A. R., "On Eccentric Digraphs of Graphs,"

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