Open Access

# A simplicity criterion for symmetric operator on a graph

### Abstract

In the present paper we show that the topology of the underlying graph determines the domain and deficiency indices of a certain associated minimal symmetric operator. We obtaine a criterion of simplicity for the minimal operator associated with the graph.

Key words: Laplace operator, quantum graph, symmetric operator, deficiency indices.

### Article Information

 Title A simplicity criterion for symmetric operator on a graph Source Methods Funct. Anal. Topology, Vol. 20 (2014), no. 2, 117-123 MathSciNet MR3242860 zbMATH 1313.47093 Milestones Received 28/10/2013; Revised 12/11/2013 Copyright The Author(s) 2014 (CC BY-SA)

E. N. Ashurova

A. N. Kandagura

I. I. Karpenko

### Citation Example

E. N. Ashurova, A. N. Kandagura, and I. I. Karpenko, A simplicity criterion for symmetric operator on a graph, Methods Funct. Anal. Topology 20 (2014), no. 2, 117-123.

### BibTex

@article {MFAT720,
AUTHOR = {Ashurova, E. N. and Kandagura, A. N. and Karpenko, I. I.},
TITLE = {A simplicity criterion for symmetric operator on a graph},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {20},
YEAR = {2014},
NUMBER = {2},
PAGES = {117-123},
ISSN = {1029-3531},
MRNUMBER = {MR3242860},
ZBLNUMBER = {1313.47093},
URL = {http://mfat.imath.kiev.ua/article/?id=720},
}