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Page 13 of Tropical Algebraic Geometry by Itenberg, Mikhalkin, and Shustin mentions 1-valent vertices, but I haven't been able to find a source that actually defines this term or managed to guess the definition myself. Either a definition or reference would be greatly appreciated. Thanks!

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Valency is sometimes used in graph theory to mean the degree of a vertex, i.e. the number of edges incident on it. – Rahul Oct 21 '10 at 4:20
Thanks. If you want to post that as an answer I can accept it so that this question won't keep popping up on the main page. – WWright Oct 21 '10 at 4:31
Somewhat related: in chemistry the concept of "valence" is the number of bonds one can associate to an atom, e.g. carbon has a valence of four since four single bonds can be attached to it. I have a feeling this was borrowed terminology. – J. M. Oct 21 '10 at 4:39
...or another way of putting it: carbon is "tetravalent". :) – J. M. Oct 21 '10 at 5:02
I feel like I should have figured out to manipulate 'valent' to 'valency' but I guess it's clear I'm no English major. This makes me kind of regret dodging intro chemistry all this time. :) – WWright Oct 22 '10 at 21:36
up vote 6 down vote accepted

In graph theory, the valency of a vertex is sometimes used to mean its degree, i.e. the number of edges incident on it. Both Wikipedia and MathWorld mention both terms as synonyms.

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