The Structure of Trivalent Graphs with Minimal Eigenvalue Gap

  • Authors:

  • Barry Guiduli

  • Affiliations:

  • Department of Mathematics, University of Chicago, Chicago, IL 60637. E-mail: bdg@math.uchicago.edu

  • Venue:
  • Journal of Algebraic Combinatorics: An International Journal
  • Year:
  • 1997

Quantified Score

Hi-index 0.00

Visualization

Abstract

Let G be a connected trivalent graph on nvertices (n \ge 10) such that among all connected trivalentgraphs on n vertices, G has the largest possiblesecond eigenvalue. We show that G must be {\it reduced\path-like}, i.e. G must be of the form:where theends are one of the following:(the right-hand end block is the mirror image of one of the blocks shown)and the middle blocks are one of the following:This partially solves a conjecture implicit in a paper of Bussemaker,Čobeljić, Cvetković, and Seidel [3].