Double-super-connected digraphs☆

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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.

Keywords

Super-connected
Double-super-connected
Line digraphs
Cartesian product
Lexicographic product

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The research was supported by the research fund for the doctoral program of Xinjiang Normal University (xjnubs0908), NSFC (10971255), the Key Project of Chinese Ministry of Education (208161), Program for New Century Excellent Talents in University, and the Project-sponsored by SRF for ROCS, SEM.

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