On super vertex-graceful unicyclic graphs

Title:

On super vertex-graceful unicyclic graphs

Creator:

Lee, Sin-Min, Leung, Elo, and Ng, Ho Kuen

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:e17160a3-6cfa-4ef4-883a-cb21fc625ecd
uuid:e17160a3-6cfa-4ef4-883a-cb21fc625ecd

Subject:

graceful, edge-graceful, super edge-graceful, super vertex-graceful, amalgamation, trees, and unicyclic graphs

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

A graph $G$ with $p$ vertices and $q$ edges, vertex set $V(G)$ and edge set $E(G)$, is said to be super vertex-graceful (in short SVG), if there exists a function pair $(f, f^+)$ where $f$ is a bijection from $V(G)$ onto $P$, $f^+$ is a bijection from $E(G)$ onto $Q$, $f^+((u, v)) = f(u) + f(v)$ for any $(u, v) \in E(G)$, $$ Q = \begin{cases} \{\pm 1,\dots , \pm \frac 12q\},&\text {if $q$ is even,}\\ \{0, \pm 1, \dots , \pm \frac 12(q-1)\},&\text {if $q$ is odd,} \end{cases} $$ and $$ P = \begin{cases} \{\pm 1,\dots , \pm \frac 12p\},&\text {if $p$ is even,}\\ \{0, \pm 1, \dots , \pm \frac 12(p-1)\},&\text {if $p$ is odd.} \end{cases} $$ \endgraf We determine here families of unicyclic graphs that are super vertex-graceful.

Language:

English

Rights:

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

Coverage:

1-22

Source:

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

Harvested from:

CDK

Metadata only:

false