1. Degree sequence for k-arc strongly connected multiple digraphs.
- Author
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Hong, Yanmei and Liu, Qinghai
- Subjects
- *
DIRECTED graphs , *PATHS & cycles in graph theory , *TOPOLOGICAL degree , *MATHEMATICAL sequences , *GRAPH connectivity - Abstract
Let D be a digraph on $\{v_{1},\ldots, v_{n}\}$ . Then the sequence $\{ (d^{+}(v_{1}), d^{-}(v_{1})), \ldots, (d^{+}(v_{n}), d^{-}(v_{n}))\}$ is called the degree sequence of D. For any given sequence of pairs of integers $\mathbf{d}=\{(d_{1}^{+}, d_{1}^{-}), \ldots, (d_{n}^{+}, d_{n}^{-})\}$ , if there exists a k-arc strongly connected digraph D such that d is the degree sequence of D, then d is realizable and D is a realization of d. In this paper, characterizations for k-arc-connected realizable sequences and realizable sequences with arc-connectivity exactly k are given. [ABSTRACT FROM AUTHOR]
- Published
- 2017
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