Minimum size of a graph or digraph of given radius

被引：8

作者：

Dankelmann, Peter ^{[1
]}

Volkmann, Lutz ^{[2
]}

机构：

[1] Univ KwaZulu Natal, Sch Math Sci, ZA-4000 Durban, South Africa

[2] Rhein Westfal TH Aachen, Lehrstuhl Math 2, D-52056 Aachen, Germany

来源：

INFORMATION PROCESSING LETTERS | 2009年 / 109卷 / 16期

关键词：

Interconnection networks; Graph; Digraph; Radius; Minimum degree; Size;

D O I：

10.1016/j.ipl.2009.06.001

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

In this paper we show that a connected graph of order n, radius r and minimum degree delta has at least 1/2 (delta n + (n-1)(delta-2)/(delta-1)(r)-1) edges, for n large enough, and this bound is sharp. We also present a similar result for digraphs. (C) 2009 Elsevier B.V. All rights reserved.

引用

页码：971 / 973

页数：3

共 50 条

[1] THE MINIMUM SIZE OF A GRAPH WITH GIVEN TREE CONNECTIVITY
Sun, Yuefang
Sheng, Bin
Jin, Zemin
DISCUSSIONES MATHEMATICAE GRAPH THEORY, 2021, 41 (02) : 409 - 425
[2] On the minimum spectral radius of connected graphs of given order and size
Cioaba, Sebastian M.
Gupta, Vishal
Marques, Celso
SPECIAL MATRICES, 2024, 12 (01):
[3] FINDING A MINIMUM EQUIVALENT GRAPH OF A DIGRAPH
MARTELLO, S
TOTH, P
NETWORKS, 1982, 12 (02) : 89 - 100
[4] AN ALGORITHM FOR FINDING A MINIMUM EQUIVALENT GRAPH OF A DIGRAPH
MOYLES, DM
THOMPSON, GL
JOURNAL OF THE ACM, 1969, 16 (03) : 455 - &
[5] NUMBER OF EDGES IN A GRAPH OF A GIVEN RADIUS
VIZING, VG
DOKLADY AKADEMII NAUK SSSR, 1967, 173 (06): : 1245 - &
[6] The minimum restricted edge-connected graph and the minimum size of graphs with a given edge-degree
Yang, Weihua
Tian, Yingzhi
Li, Hengzhe
Li, Hao
Guo, Xiaofeng
DISCRETE APPLIED MATHEMATICS, 2014, 167 : 304 - 309
[7] On size, radius and minimum degree
Mukwembi, Simon
DISCRETE MATHEMATICS AND THEORETICAL COMPUTER SCIENCE, 2014, 16 (01): : 1 - 5
[8] MINIMUM BLOCK CONTAINING A GIVEN GRAPH
PLESNIK, J
ARCHIV DER MATHEMATIK, 1976, 27 (06) : 668 - 672
[9] The number of edges in a bipartite graph of given radius
Dankelmann, P.
Swart, Henda C.
van den Berg, P.
DISCRETE MATHEMATICS, 2011, 311 (8-9) : 690 - 698
[10] Maximum size of digraphs of given radius
Cambie, Stijn
DISCRETE MATHEMATICS, 2023, 346 (08)

← 1 2 3 4 5 →