On $k$-pairable graphs from trees

Title:

On $k$-pairable graphs from trees

Creator:

Che, Zhongyuan

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:1a8c98eb-5582-4d7e-a9a8-640522eb0757
uuid:1a8c98eb-5582-4d7e-a9a8-640522eb0757

Subject:

$k$-pairable graph;, pair length, Cartesian product, $G$-layer, and tree

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

The concept of the $k$-pairable graphs was introduced by Zhibo Chen (On $k$-pairable graphs, Discrete Mathematics 287 (2004), 11–15) as an extension of hypercubes and graphs with an antipodal isomorphism. In the same paper, Chen also introduced a new graph parameter $p(G)$, called the pair length of a graph $G$, as the maximum $k$ such that $G$ is $k$-pairable and $p(G)=0$ if $G$ is not $k$-pairable for any positive integer $k$. In this paper, we answer the two open questions raised by Chen in the case that the graphs involved are restricted to be trees. That is, we characterize the trees $G$ with $p(G)=1$ and prove that $p(G \square H)=p(G)+p(H)$ when both $G$ and $H$ are trees.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

377-386

Source:

Czechoslovak Mathematical Journal | 2007 Volume:57 | Number:1

Harvested from:

CDK

Metadata only:

false