|
| | | | |
| | | |
| Stat |
Members: 3645
Articles: 2'500'096
Articles rated: 2609
19 April 2024 |
|
| | | | |
|
Article overview
| |
|
|
A differential approach for bounding the index of graphs under perturbations | | C. Dalfó
; M.A. Fiol
; E. Garriga
; | | Date: |
23 Sep 2012 | | Abstract: | This paper presents bounds for the variation of the spectral radius
$lambda(G)$ of a graph $G$ after some perturbations or local vertex/edge
modifications of $G$. The perturbations considered here are the connection of a
new vertex with, say, $g$ vertices of $G$, the addition of a pendant edge (the
previous case with $g=1$) and the addition of an edge. The method proposed here
is based on continuous perturbations and the study of their differential
inequalities associated. Within rather economical information (namely, the
degrees of the vertices involved in the perturbation), the best possible
inequalities are obtained. In addition, the cases when equalities are attained
are characterized. The asymptotic behavior of the bounds obtained is also
discussed. For instance, if $G$ is a connected graph and $G_u$ denotes the
graph obtained from $G$ by adding a pendant edge at vertex $u$ with degree
$delta_u$, then, $$ lambda(G_u)le
lambda(G)+frac{delta_u}{lambda^3(G)}+ extrm{o}(frac{1}{lambda^3(G)}). $$ | | Source: | arXiv, 1209.5047 | | Services: | Forum | Review | PDF | Favorites | |
|
|
No review found.
Did you like this article?
Note: answers to reviews or questions about the article must be posted in the forum section.
Authors are not allowed to review their own article. They can use the forum section.
browser claudebot
|
| |
|
|
|
|
News, job offers and information for researchers and scientists:
| |
REGISTER