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# Branch

In complex analysis, a branch (also called a sheet) is a portion of the range of a multivalued function over which the function is single-valued. Combining all the sheets gives the full structure of the function. It is often convenient to choose a particular branch of a function to work with, and this choice is often designated the "principal branch" (or "principal sheet").

In graph theory, a branch at a point in a tree is a maximal subtree containing as an endpoint (Harary 1994, p. 35).

Bifurcation, Branch Cut, Branch Point, Fork, Tree Leaf, Limb, Multivalued Function, Principal Branch, Tree

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## References

Harary, F. Graph Theory. Reading, MA: Addison-Wesley, 1994.Lu, T. "The Enumeration of Trees with and without Given Limbs." Disc. Math. 154, 153-165, 1996.Schwenk, A. "Almost All Trees are Cospectral." In New Directions in the Theory of Graphs (Ed. F. Harary). New York: Academic Press, pp. 275-307, 1973.

Branch

## Cite this as:

Weisstein, Eric W. "Branch." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Branch.html