Minimally strong digraphs

Author:

Geller Dennis P.

Abstract

Dirac (2) and Plummer (5) independently investigated the structure of minimally 2-connected graphs G, which are characterized by the property that for any line x of G, G–x is not 2-connected. In this paper we investigate an analogous class of strongly connected digraphs D such that for any arc x, D–x is not strong. Not surprisingly, these digraphs have much in common with the minimally 2-connected graphs, and a number of theorems similar to those in (2) and (5) are proved, notably our Theorems 9 and 12.

Publisher

Cambridge University Press (CUP)

Subject

General Mathematics

Reference6 articles.

1. On blocks with a minimal number of lines;Plummer;Trans. Amer. Math. Soc.

2. GRAPH THEORY

3. A Theorem on Graphs, with an Application to a Problem of Traffic Control

4. Minimally 2-connected graphs;Dirac;J. reine angew. Math.,1968

Cited by 10 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Structural properties of minimal strong digraphs versus trees;Linear Algebra and its Applications;2018-03

2. Minimal strong digraphs;Discrete Mathematics;2012-02

3. Introduction;Graphs and Order;1985

4. On minimal strong blocks;Journal of Graph Theory;1979

5. The minimum degree and connectivity of a graph;Lecture Notes in Mathematics;1978

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