Spectral spread of Graphs
碩士 === 國立交通大學 === 應用數學系所 === 100 === Abstract Given an n×n matrixM, the spread, φ(M), is essentially the diameter of its spectrum: φ(M) := max i;j |ρi − ρj |, where the maximal is taken over all pairs of eigenvalues (or nonzero eigenvalues in some cases) of M. We consider adjacent matrices, Laplacia...
| Main Authors: | , |
|---|---|
| Other Authors: | |
| Format: | Others |
| Language: | zh-TW |
| Published: |
2011
|
| Online Access: | http://ndltd.ncl.edu.tw/handle/07455290033859070793 |
| Summary: | 碩士 === 國立交通大學 === 應用數學系所 === 100 === Abstract
Given an n×n matrixM, the spread, φ(M), is essentially the diameter of its spectrum:
φ(M) := max
i;j
|ρi − ρj |,
where the maximal is taken over all pairs of eigenvalues (or nonzero eigenvalues in
some cases) of M. We consider adjacent matrices, Laplacian and signless Laplacian
matrices which are commonly used in graph theory. After discussing relatedness on
the graphs and their corresponding spreads, we discover the boundary which affects
the spread, and use this result to find the graphs that may have the maximal or
minimal spread.
|
|---|