Results on $F$-continuous graphs

Title:

Results on $F$-continuous graphs

Creator:

Draganova, Anna

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:902f9f4d-9b97-419d-a15a-035b1692613a
uuid:902f9f4d-9b97-419d-a15a-035b1692613a

Subject:

continuous, $F$-continuous, $F$-regular, and regular graph

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

For any nontrivial connected graph $F$ and any graph $G$, the {\it $F$-degree} of a vertex $v$ in $G$ is the number of copies of $F$ in $G$ containing $v$. $G$ is called {\it $F$-continuous} if and only if the $F$-degrees of any two adjacent vertices in $G$ differ by at most 1; $G$ is {\it $F$-regular} if the $F$-degrees of all vertices in $G$ are the same. This paper classifies all $P_4$-continuous graphs with girth greater than 3. We show that for any nontrivial connected graph $F$ other than the star $K_{1,k}$, $k \geq 1$, there exists a regular graph that is not $F$-continuous. If $F$ is 2-connected, then there exists a regular $F$-continuous graph that is not $F$-regular.

Language:

English

Rights:

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

Coverage:

51-60

Source:

Czechoslovak Mathematical Journal | 2009 Volume:59 | Number:1

Harvested from:

CDK

Metadata only:

false