SIZE OF GRAPHS AND DIGRAPHS WITH GIVEN DIAMETER AND CONNECTIVITY CONSTRAINTS

被引:0
作者
Dankelmann, P. [1 ]
机构
[1] Univ Johannesburg, Dept Math & Appl Math, POB 524, ZA-2006 Auckland Pk, South Africa
基金
新加坡国家研究基金会;
关键词
diameter; connectivity; edge-connectivity; graph; digraph; Eulerian digraph; MAXIMUM; ORDER;
D O I
10.1007/s10474-021-01137-7
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We determine the maximum size of a graph of given order, diameter, and edge-connectivity lambda for 2 <= lambda <= 7. This completes the determination of the maximum size of graphs with given order, diameter and edge-connectivity lambda which had previously been done for lambda = 1 and lambda >= 8. We further prove that upper bounds on the size of a graph of given order and diameter having certain additional properties can be extended to Eulerian digraphs, provided the additional properties satisfy some mild conditions. As an application of this result we prove that upper bounds on the size of graphs with given order, diameter and either edge-connectivity, connectivity, or minimum degree can be extended to Eulerian digraphs.
引用
收藏
页码:178 / 199
页数:22
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