若干有向卡氏积图类广义3-弧强连通度的精确值
Precise Values for the Generalized 3-Arc-Connectivity of Cartesian Product of Some Digraph Classes
摘要: 无向图G的广义k-边连通度的定义是1985年由Hager引入的,这个定义后来又被人们推广到有向图中,并相应定义了有向图中的广义k-弧强连通度。近年来,广义k-弧强连通度的研究得到了很多重要的结果。在本文中,我们给出了某些有向卡氏积图类的3-弧强连通度的精确值。
Abstract:
The definition of generalized k-edge connectivity of undirected graph G was introduced by Hager in 1985. This concept was extended to directed graph and the definition of generalized k-arc- connectivity was proposed. In recent years, the study of generalized k-arc-connectivity has achieved many important results. In this paper, we give precise values for the generalized 3-arc-connectivity of Cartesian product of some digraph classes.
参考文献
|
[1]
|
Bang-Jensen, J. and Gutin, G. (2009) Digraphs: Theory, Algorithms and Applications. 2nd Edition, Springer, London. [Google Scholar] [CrossRef]
|
|
[2]
|
Bondy, J.A. and Murty, U.S.R. (2008) Graph Theory. Springer, Berlin.
|
|
[3]
|
Hager, M. (1985) Pendant Tree-Connectivity. Journal of Combinatorial Theory, Series B, 38,179-189. [Google Scholar] [CrossRef]
|
|
[4]
|
Li, X., Mao, Y. and Sun, Y. (2014) On the Generalized (Edge-)Connectivity of Graphs. Australasian Journal of Combinatorics, 58, 304-319.
|
|
[5]
|
Li, X. and Mao, Y. (2016) Generalized Connectivity of Graphs. Springer, Switzerland. [Google Scholar] [CrossRef]
|
|
[6]
|
Sun, Y. and Yeo, A. (2022) Directed Steiner Tree Packing and Directed Tree Connectivity. Journal of Graph Theory, 101, 1-21. [Google Scholar] [CrossRef]
|
|
[7]
|
Sun, Y.F. (2022) Extremal Results for Directed Tree Connectivity. Bulletin of the Malaysian Mathematical Sciences Society, 45, 839-850. [Google Scholar] [CrossRef]
|
|
[8]
|
Sun, Y. (2022) Steiner Type Packing Problems in Di-graphs: A Survey, arXiv:2206.12092v1.
|
|
[9]
|
Hammack, R.H. (2018) Digraphs Products. In: Bang-Jensen, J. and Gutin, G., Eds., Classes of Directed Graphs, Springer, London. [Google Scholar] [CrossRef]
|