Double-super-connected digraphs

Authors:
Juan Liu;Jixiang Meng;Zhao Zhang
Affiliations:
College of Mathematics-Physics and Information Sciences, Xinjiang Normal University, Urumqi, Xinjiang, 830054, PR China and College of Mathematics and System Sciences, Xinjiang University, Urumqi, ...;College of Mathematics and System Sciences, Xinjiang University, Urumqi, Xinjiang, 830046, PR China;College of Mathematics and System Sciences, Xinjiang University, Urumqi, Xinjiang, 830046, PR China
Venue:
Discrete Applied Mathematics
Year:
2010

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Abstract

A strongly connected digraph D is said to be super-connected if every minimum vertex-cut is the out-neighbor or in-neighbor set of a vertex. A strongly connected digraph D is said to be double-super-connected if every minimum vertex-cut is both the out-neighbor set of a vertex and the in-neighbor set of a vertex. In this paper, we characterize the double-super-connected line digraphs, Cartesian product and lexicographic product of two digraphs. Furthermore, we study double-super-connected Abelian Cayley digraphs and illustrate that there exist double-super-connected digraphs for any given order and minimum degree.