# On a poset of trees

@article{Csikvri2010OnAP, title={On a poset of trees}, author={P{\'e}ter Csikv{\'a}ri}, journal={Combinatorica}, year={2010}, volume={30}, pages={125-137} }

- Published 2010 in Combinatorica
DOI:10.1007/s00493-010-2516-0

We will prove that the path minimizes the number of closed walks of length l among the connected graphs for all l. Indeed, we will prove that the number of closed walks of length l and many other properties such as the spectral radius, Estada index increase or decrease along a certain poset of trees. This poset is a leveled poset with path as the smallest element and star as the greatest element.

#### Citations

##### Publications citing this paper.

Showing 1-9 of 9 extracted citations

## Walks and paths in trees

View 12 Excerpts

Highly Influenced

## Graph-indexed random walks on special classes of graphs

View 1 Excerpt

## Immanantal polynomials and the GTS poset on Trees

View 2 Excerpts

## Homomorphisms of Trees into a Path

View 4 Excerpts

## Graph Homomorphisms between Trees

View 8 Excerpts

## On the roots of edge cover polynomials of graphs

View 1 Excerpt

#### References

##### Publications referenced by this paper.

Showing 1-10 of 15 references

## On graphs with randomly deleted edges

View 7 Excerpts

Highly Influenced

## A proof of a conjecture on the Estrada index , MATCH Commun

## Estimating the Estrada index, Linear Algebra and its Applications

View 2 Excerpts

## Subgraph centrality in complex networks.

View 1 Excerpt

## Some Inequalities For The Largest Eigenvalue Of A Graph

View 1 Excerpt

## Characterization of 3D molecular structure

View 1 Excerpt

## Combinatorial problems and exercises (2. ed.)

View 1 Excerpt