On super vertex-graceful unicyclic graphs

Sin Min Lee; Elo Leung; Ho Kuen Ng

Czechoslovak Mathematical Journal (2009)

  • Volume: 59, Issue: 1, page 1-22
  • ISSN: 0011-4642

Abstract

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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 ) ∈ E ( G ) , Q = { ± 1 , ⋯ , ± 1 2 q } , if q is even, { 0 , ± 1 , ⋯ , ± 1 2 ( q - 1 ) } , if q is odd, and P = { ± 1 , ⋯ , ± 1 2 p } , if p is even, { 0 , ± 1 , ⋯ , ± 1 2 ( p - 1 ) } , if p is odd. We determine here families of unicyclic graphs that are super vertex-graceful.

How to cite

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Lee, Sin Min, Leung, Elo, and Ng, Ho Kuen. "On super vertex-graceful unicyclic graphs." Czechoslovak Mathematical Journal 59.1 (2009): 1-22. <http://eudml.org/doc/37904>.

@article{Lee2009,
abstract = {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 $(u, v) \in E(G)$, \[ Q = \{\left\lbrace \begin\{array\}\{ll\} \lbrace \pm 1,\dots , \pm \frac\{1\}\{2\}q\rbrace ,&\text\{if $q$ is even,\}\\ \lbrace 0, \pm 1, \dots , \pm \frac\{1\}\{2\}(q-1)\rbrace ,&\text\{if $q$ is odd,\} \end\{array\}\right.\} \] and \[ P = \{\left\lbrace \begin\{array\}\{ll\} \lbrace \pm 1,\dots , \pm \frac\{1\}\{2\}p\rbrace ,&\text\{if $p$ is even,\}\\ \lbrace 0, \pm 1, \dots , \pm \frac\{1\}\{2\}(p-1)\rbrace ,&\text\{if $p$ is odd.\} \end\{array\}\right.\} \] We determine here families of unicyclic graphs that are super vertex-graceful.},
author = {Lee, Sin Min, Leung, Elo, Ng, Ho Kuen},
journal = {Czechoslovak Mathematical Journal},
keywords = {graceful; edge-graceful; super edge-graceful; super vertex-graceful; amalgamation; trees; unicyclic graphs; graceful; edge-graceful; super edge-graceful; super vertex-graceful; amalgamation; tree; unicyclic graph},
language = {eng},
number = {1},
pages = {1-22},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On super vertex-graceful unicyclic graphs},
url = {http://eudml.org/doc/37904},
volume = {59},
year = {2009},
}

TY - JOUR
AU - Lee, Sin Min
AU - Leung, Elo
AU - Ng, Ho Kuen
TI - On super vertex-graceful unicyclic graphs
JO - Czechoslovak Mathematical Journal
PY - 2009
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 59
IS - 1
SP - 1
EP - 22
AB - 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 $(u, v) \in E(G)$, \[ Q = {\left\lbrace \begin{array}{ll} \lbrace \pm 1,\dots , \pm \frac{1}{2}q\rbrace ,&\text{if $q$ is even,}\\ \lbrace 0, \pm 1, \dots , \pm \frac{1}{2}(q-1)\rbrace ,&\text{if $q$ is odd,} \end{array}\right.} \] and \[ P = {\left\lbrace \begin{array}{ll} \lbrace \pm 1,\dots , \pm \frac{1}{2}p\rbrace ,&\text{if $p$ is even,}\\ \lbrace 0, \pm 1, \dots , \pm \frac{1}{2}(p-1)\rbrace ,&\text{if $p$ is odd.} \end{array}\right.} \] We determine here families of unicyclic graphs that are super vertex-graceful.
LA - eng
KW - graceful; edge-graceful; super edge-graceful; super vertex-graceful; amalgamation; trees; unicyclic graphs; graceful; edge-graceful; super edge-graceful; super vertex-graceful; amalgamation; tree; unicyclic graph
UR - http://eudml.org/doc/37904
ER -

References

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