A simple digraph D (without loops and multiple arcs) is said to be super-connected if every minimum vertex-cut is the out-neighbor set or in-neighbor set of a vertex. A super-connected digraph D is said to be bi-super-connected if there exists a minimum vertex-cut is both the out-neighbor set of a vertex and the in-neighbor set of a vertex. In this paper, we will give the necessary and sufficient conditions of line digraph is bi-super-connected, furthermore, we study the big super-connectivity of Cartesian product and lexicographic product of two digraphs.
LI Jing-Jing
,
LIU Juan
. Bi-super-connected digraphs[J]. Journal of East China Normal University(Natural Science), 2016
, 2016(1)
: 91
-95
.
DOI: 10.3969/j.issn.1000-5641.2016.01.011
[1]MENG J X, ZHANG Z. Super-connected arc-transitive digraphs [J].Discrete Applied Mathematics, 2009, 157: 653-658.
[2]CHIUE W S, SHIEH B S. On connectivity of the Cartesian product oftwo graphs [J]. Applied Mathematics and Computation, 1999, 102:
129-137.
[3]XU J M, YANG C. Connectivity of Cartesian product graphs [J].Discrete Mathematics, 2006, 306: 159-165.
[4]MENG J X. Superconnectivity and super edge-connectivity of linegraphs [J]. Graph Theory Notes of New York, XL 2001: 12-14.
[5]XU J M, LV M, MA M J, HElLLWIG A. Super connectivity of line graphs[J]. Information Processing Letters, 2005, 94: 191-195.
[6]ZHANG Z, LIU F X, MENG J X. Super-connected $n$-th interated linedigraphs [J]. OR Transanctions, 2005, 9: 35-39.
[7]SHIEH B S. Super edge- and point-connectivities of the Cartesianproduct of regular graphs [J]. Networks, 2002, 40: 91-96.
[8]LIU J, MENG J X. Super-connected and super-arc-connected Cartesianproduct of digraphs [J]. Information Processing Letters, 2008, 108:
90-93.
[9]LIU J, MENG J X, ZHANG Z. Double-super-connected digraph [J].Discrete Applied Mathematics, 2010, 158: 1012-1016.
[10]XU J M. Topological Structure and Analysis of InterconnectionNetworks [M]. Dordrecht, Netherlands: Kluwer Academic Publishers,
2001.
中国综合性科技类核心期刊(北大核心)