#### Title

On induced subdigraphs of certain distance-defined digraphs

#### Abbreviated Journal Title

Util. Math.

#### Keywords

peripheral vertex; eccentric vertex; boundary vertex; antipodal digraph; eccentric digraph; boundary digraph; GRAPHS; VERTICES; Mathematics, Applied; Statistics & Probability

#### Abstract

Let G be a nontrivial connected graph. A vertex v is a boundary vertex of a vertex u and of G if d(u, w) <= d(u, v) for all neighbors w of v. The boundary digraph BD(G) of G is that digraph with vertex set V(G), where (u, v) is an arc of BD(G) if v is a boundary vertex of u. We investigate the problem of determining which digraphs are the induced subdigraph of the boundary digraph of some graph. We also consider that problem for other distance-related digraphs. For a digraph D, the embedding number of D is the smallest order of a graph G such that D is an induced subdigraph of BD(G). We establish bounds for the embedding numbers of some classes of digraphs.

#### Journal Title

Utilitas Mathematica

#### Volume

68

#### Publication Date

1-1-2005

#### Document Type

Article

#### Language

English

#### First Page

239

#### Last Page

253

#### WOS Identifier

#### ISSN

0315-3681

#### Recommended Citation

"On induced subdigraphs of certain distance-defined digraphs" (2005). *Faculty Bibliography 2000s*. 5013.

http://stars.library.ucf.edu/facultybib2000/5013

## Comments

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