About Kronrod-Reeb graph of a function on a manifold

Authors

  • V. V. Sharko Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereshchenkivs'ka, Kyiv, 01601, Ukraine 

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Abstract

We study Kronrod-Reeb graphs of functions with isolated critical points on smooth manifolds. We prove that any finite graph, which satisfies the condition $\Im$ is a Kronrod-Reeb graph for some such function on some manifold. In this connection, monotone functions on graphs are investigated.

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Published

2006-12-25

Issue

Vol. 12 No. 4 (2006)

Section

Articles

How to Cite

Sharko, V. V. “About Kronrod-Reeb Graph of a Function on a Manifold”. Methods of Functional Analysis and Topology, vol. 12, no. 4, Dec. 2006, pp. 389-96, https://zen.imath.kiev.ua/index.php/mfat/article/view/331.