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.

Full Text

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},
  MRNUMBER = {MR2279875},
       URL = {http://mfat.imath.kiev.ua/article/?id=398},
}