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Why is "Handshaking lemma" trending?

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  • Ranking position: #
  • Date: 2026-04-14 14:17:36

This topic has appeared in the trending rankings 1 time(s) in the past year. While it does not trend frequently, its appearance suggests a renewed or concentrated surge of public interest.

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Handshaking lemma

Wikipedia Overview

In graph theory, the handshaking lemma is the statement that, in every finite undirected graph, the number of vertices that touch an odd number of edges is even. For example, if there is a party of people who shake hands, the number of people who shake an odd number of other people's hands is even. The handshaking lemma is a consequence of the degree sum formula, also sometimes called the handshaking lemma, according to which the sum of the degrees equals twice the number of edges in the graph. Both results were proven by Leonhard Euler in his famous paper on the Seven Bridges of Königsberg that began the study of graph theory.

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