Open Access

About Kronrod-Reeb graph of a function on a manifold

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.

Article Information

 Title About Kronrod-Reeb graph of a function on a manifold Source Methods Funct. Anal. Topology, Vol. 12 (2006), no. 4, 389-396 MathSciNet MR2279875 Copyright The Author(s) 2006 (CC BY-SA)

Authors Information

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

Citation Example

V. V. Sharko, About Kronrod-Reeb graph of a function on a manifold, Methods Funct. Anal. Topology 12 (2006), no. 4, 389-396.

BibTex

@article {MFAT398,
AUTHOR = {Sharko, V. V.},
TITLE = {About Kronrod-Reeb graph of a function on a manifold},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {12},
YEAR = {2006},
NUMBER = {4},
PAGES = {389-396},
ISSN = {1029-3531},
URL = {http://mfat.imath.kiev.ua/article/?id=398},
}