Minimum size of a graph or digraph of given radius

Peter Dankelmann; Lutz Volkmann

doi:10.1016/j.ipl.2009.06.001

Minimum size of a graph or digraph of given radius

Peter Dankelmann, Lutz Volkmann

Research output: Contribution to journal › Article › peer-review

8 Citations (Scopus)

Abstract

In this paper we show that a connected graph of order n, radius r and minimum degree δ has at least frac(1, 2) (δ n + frac((n - 1) (δ - 2), (δ - 1)^r - 1)) edges, for n large enough, and this bound is sharp. We also present a similar result for digraphs.

Original language	English
Pages (from-to)	971-973
Number of pages	3
Journal	Information Processing Letters
Volume	109
Issue number	16
DOIs	https://doi.org/10.1016/j.ipl.2009.06.001
Publication status	Published - 31 Jul 2009
Externally published	Yes

Keywords

Digraph
Graph
Interconnection networks
Minimum degree
Radius
Size

ASJC Scopus subject areas

Theoretical Computer Science
Signal Processing
Information Systems
Computer Science Applications

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10.1016/j.ipl.2009.06.001

Cite this

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abstract = "In this paper we show that a connected graph of order n, radius r and minimum degree δ has at least frac(1, 2) (δ n + frac((n - 1) (δ - 2), (δ - 1)r - 1)) edges, for n large enough, and this bound is sharp. We also present a similar result for digraphs.",

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author = "Peter Dankelmann and Lutz Volkmann",

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AU - Dankelmann, Peter

AU - Volkmann, Lutz

PY - 2009/7/31

Y1 - 2009/7/31

N2 - In this paper we show that a connected graph of order n, radius r and minimum degree δ has at least frac(1, 2) (δ n + frac((n - 1) (δ - 2), (δ - 1)r - 1)) edges, for n large enough, and this bound is sharp. We also present a similar result for digraphs.

AB - In this paper we show that a connected graph of order n, radius r and minimum degree δ has at least frac(1, 2) (δ n + frac((n - 1) (δ - 2), (δ - 1)r - 1)) edges, for n large enough, and this bound is sharp. We also present a similar result for digraphs.

KW - Digraph

KW - Graph

KW - Interconnection networks

KW - Minimum degree

KW - Radius

KW - Size

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U2 - 10.1016/j.ipl.2009.06.001

DO - 10.1016/j.ipl.2009.06.001

M3 - Article

AN - SCOPUS:67649340794

SN - 0020-0190

VL - 109

SP - 971

EP - 973

JO - Information Processing Letters

JF - Information Processing Letters

IS - 16

ER -

Minimum size of a graph or digraph of given radius

Abstract

Keywords

ASJC Scopus subject areas

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