# Minimum degree spanning tree

In graph theory, for a connected graph ${\displaystyle G}$, a spanning tree ${\displaystyle T}$ is a subgraph of ${\displaystyle G}$ with the least number of edges that still spans ${\displaystyle G}$. A number of properties can be proved about ${\displaystyle T}$. ${\displaystyle T}$ is acyclic, has (${\displaystyle |V|-1}$) edges where ${\displaystyle V}$ is the number of vertices in ${\displaystyle G}$ etc.

A minimum degree spanning tree ${\displaystyle T'}$ is a spanning tree which has the least maximum degree. The vertex of maximum degree in ${\displaystyle T'}$ is the least among all possible spanning trees of ${\displaystyle G}$.

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