| Title:
|
On super vertex-graceful unicyclic graphs (English) |
| Author:
|
Lee, Sin-Min |
| Author:
|
Leung, Elo |
| Author:
|
Ng, Ho Kuen |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
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59 |
| Issue:
|
1 |
| Year:
|
2009 |
| Pages:
|
1-22 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
graceful |
| Keyword:
|
edge-graceful |
| Keyword:
|
super edge-graceful |
| Keyword:
|
super vertex-graceful |
| Keyword:
|
amalgamation |
| Keyword:
|
trees |
| Keyword:
|
unicyclic graphs |
| MSC:
|
05C78 |
| idZBL:
|
Zbl 1224.05447 |
| idMR:
|
MR2486612 |
| . |
| Date available:
|
2010-07-20T14:47:47Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140458 |
| . |
| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| Reference:
|
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| Reference:
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|
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|
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|
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|
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