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arXiv · 1512.01377

On connected simple graphs and their degree sequences

Jonathan McLaughlin
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Abstract

This note describes necessary and sufficient conditions for a sequence of positive integers to be the degree sequence of a connected simple graph. Conditions are also given under which a sequence is necessarily connected i.e. the sequence can only be realised as a connected graph. A matrix is introduced whose non-empty entries partition the set of connected graphs. The note concludes with a result relating the number of edges in a simple graph to the connectedness of the graph.

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Jonathan McLaughlin. 2015-12-17. On connected simple graphs and their degree sequences. https://arxiv.org/abs/1512.01377

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