Non-bipartiteness of graphs and the upper bounds of Dirichlet forms

Yusuke Higuchi, Tomoyuki Shirai

Research output: Contribution to journalArticle

Abstract

The sum of the lower bound and the upper one of the spectrum of our discrete Laplacian is less than or equal to 2. The equality holds if a graph is bipartite while the converse does not hold for general infinite graphs. In this paper, we give an estimate of the upper bounds of Dirichlet forms and using this estimate together with an h-transform, we show that the sum is strictly less than 2 for a certain class of infinite graphs.

Original languageEnglish
Pages (from-to)259-268
Number of pages10
JournalPotential Analysis
Volume25
Issue number3
DOIs
Publication statusPublished - Nov 1 2006

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Dirichlet Form
Infinite Graphs
H-transform
Discrete Laplacian
Upper bound
Less than or equal to
Graph in graph theory
Converse
Estimate
Equality
Strictly
Lower bound
Class

All Science Journal Classification (ASJC) codes

  • Analysis

Cite this

Non-bipartiteness of graphs and the upper bounds of Dirichlet forms. / Higuchi, Yusuke; Shirai, Tomoyuki.

In: Potential Analysis, Vol. 25, No. 3, 01.11.2006, p. 259-268.

Research output: Contribution to journalArticle

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