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

Yusuke Higuchi, Tomoyuki Shirai

Research output: Contribution to journalArticle


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
Issue number3
Publication statusPublished - Nov 1 2006

All Science Journal Classification (ASJC) codes

  • Analysis

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