
TL;DR
This paper characterizes the existence of Eulerian circuits and paths in finite connected directed multigraphs using conditions on vertex degrees and vertex pair connectivity.
Contribution
It provides necessary and sufficient conditions for directed multigraphs to have Eulerian circuits and paths, extending classical graph theory results.
Findings
Characterization of Eulerian circuits in directed multigraphs.
Conditions for existence of Eulerian paths in directed multigraphs.
Theoretical criteria involving vertex degrees and connectivity.
Abstract
For a finite connected nontrivial directed multigraph, we prove: 1. has a directed circuit using each directed edge exactly once if and only if both each pair of distinct vertices of occur in a common directed circuit and in-degree out-degree for every vertex . 2. contains a non-circuit directed path which uses every directed edge exactly once if and only if both every pair of distinct vertices of occur in a common directed circuit and there are vertices such that in-degree out-degree out-degree in-degree but, for every vertex , it happens that in-degree out-degree.
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Taxonomy
Topicsgraph theory and CDMA systems · Graph Labeling and Dimension Problems · Advanced Graph Theory Research
