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Degree sequence for k-arc strongly connected multiple digraphs.

Yanmei Hong1, Qinghai Liu2

  • 1College of Mathematics and Computer Science, Fuzhou University, Fuzhou, 350108 P.R. China.

Journal of Inequalities and Applications
|November 7, 2017
PubMed
Summary
This summary is machine-generated.

This study characterizes degree sequences for k-arc strongly connected digraphs. It provides conditions for sequences to be realizable and defines arc-connectivity precisely.

Keywords:
degree sequencek-arc strongly connectedrealization

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Area of Science:

  • Graph Theory
  • Discrete Mathematics
  • Network Analysis

Background:

  • The degree sequence of a digraph D on n vertices is defined as the sequence of pairs of integers (out-degree, in-degree) for each vertex.
  • A degree sequence is realizable if a k-arc strongly connected digraph exists with that sequence.
  • Understanding digraph properties is crucial for network analysis and algorithm design.

Purpose of the Study:

  • To provide characterizations for realizable degree sequences in k-arc strongly connected digraphs.
  • To establish criteria for digraphs with an exact arc-connectivity of k.

Main Methods:

  • The study involves theoretical analysis of digraph properties.
  • It focuses on the relationship between degree sequences and k-arc strong connectivity.
  • Mathematical proofs are used to establish characterizations.

Main Results:

  • Characterizations for k-arc-connected realizable sequences are presented.
  • Criteria for sequences with arc-connectivity exactly k are established.
  • The paper defines conditions under which a given degree sequence corresponds to a specific level of digraph connectivity.

Conclusions:

  • The findings contribute to the theoretical understanding of digraph structures.
  • This research offers tools for constructing or analyzing digraphs with specific connectivity properties.
  • The results are foundational for further studies in network theory and algorithm development.