k-connected degree sequences
Jonathan McLaughlin
TL;DR
This paper establishes precise conditions for when a positive integer sequence can represent the degree sequence of a k-connected simple graph, including criteria for guaranteed k-connectivity.
Contribution
It provides necessary and sufficient conditions for degree sequences to correspond to k-connected graphs, advancing understanding of graph connectivity properties.
Findings
Characterization of degree sequences for k-connected graphs
Conditions ensuring a degree sequence is necessarily k-connected
Theoretical framework for graph connectivity based on degree sequences
Abstract
Necessary and sufficient conditions for a sequence of positive integers to be the degree sequence of a k-connected simple graph are detailed. Conditions are also given under which such a sequence is necessarily k-connected.
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Taxonomy
TopicsDigital Image Processing Techniques · graph theory and CDMA systems · semigroups and automata theory