Characterization of eccentric digraphs

The eccentric digraph ED(G) of a digraph G represents the binary relation, defined on the vertex set of G, of being `eccentric'; that is, there is an arc from u to v in ED(G) if and only if v is at maximum distance from u in G. A digraph G is said to be eccentric if there exists a digraph H such that G = ED(H). This paper is devoted to the study of the following two questions: what digraphs are eccentric and when the relation of being eccentric is symmetric. We present a characterization of eccentric digraphs, which in the undirected case says that a graph G is eccentric iff its complement Supported by the Ministry of Science and Technology, Spain, and the European

• Type: Journal
• Year: 2006
• Where: DM
• Authors: Joan Gimbert, Nacho López, Mirka Miller, Joseph F. Ryan
• Keywords: Binary Relation, DM 2006, Eccentric Digraphs, Maximum Distance