# On γ-labelings of trees

Gary Chartrand; David Erwin; Donald W. VanderJagt; Ping Zhang

Discussiones Mathematicae Graph Theory (2005)

- Volume: 25, Issue: 3, page 363-383
- ISSN: 2083-5892

## Access Full Article

top## Abstract

top## How to cite

topGary Chartrand, et al. "On γ-labelings of trees." Discussiones Mathematicae Graph Theory 25.3 (2005): 363-383. <http://eudml.org/doc/270423>.

@article{GaryChartrand2005,

abstract = {Let G be a graph of order n and size m. A γ-labeling of G is a one-to-one function f:V(G) → 0,1,2,...,m that induces a labeling f’: E(G) → 1,2,...,m of the edges of G defined by f’(e) = |f(u)-f(v)| for each edge e = uv of G. The value of a γ-labeling f is $val(f) = Σ_\{e ∈ E(G)\}f^\{\prime \}K(e)$. The maximum value of a γ-labeling of G is defined as
$val_\{max\}(G) = max \{val(f) : f is a γ- labeling of G\}$;
while the minimum value of a γ-labeling of G is
$val_\{min\}(G) = min \{val(f) : f is a γ- labeling of G\}$;
The values $val_\{max\}(S_\{p,q\})$ and $val_\{min\}(S_\{p,q\})$ are determined for double stars $S_\{p,q\}$. We present characterizations of connected graphs G of order n for which $val_\{min\}(G) = n$ or $val_\{min\}(G) = n+1$.},

author = {Gary Chartrand, David Erwin, Donald W. VanderJagt, Ping Zhang},

journal = {Discussiones Mathematicae Graph Theory},

keywords = {γ-labeling; value of a γ-labeling; -labelling},

language = {eng},

number = {3},

pages = {363-383},

title = {On γ-labelings of trees},

url = {http://eudml.org/doc/270423},

volume = {25},

year = {2005},

}

TY - JOUR

AU - Gary Chartrand

AU - David Erwin

AU - Donald W. VanderJagt

AU - Ping Zhang

TI - On γ-labelings of trees

JO - Discussiones Mathematicae Graph Theory

PY - 2005

VL - 25

IS - 3

SP - 363

EP - 383

AB - Let G be a graph of order n and size m. A γ-labeling of G is a one-to-one function f:V(G) → 0,1,2,...,m that induces a labeling f’: E(G) → 1,2,...,m of the edges of G defined by f’(e) = |f(u)-f(v)| for each edge e = uv of G. The value of a γ-labeling f is $val(f) = Σ_{e ∈ E(G)}f^{\prime }K(e)$. The maximum value of a γ-labeling of G is defined as
$val_{max}(G) = max {val(f) : f is a γ- labeling of G}$;
while the minimum value of a γ-labeling of G is
$val_{min}(G) = min {val(f) : f is a γ- labeling of G}$;
The values $val_{max}(S_{p,q})$ and $val_{min}(S_{p,q})$ are determined for double stars $S_{p,q}$. We present characterizations of connected graphs G of order n for which $val_{min}(G) = n$ or $val_{min}(G) = n+1$.

LA - eng

KW - γ-labeling; value of a γ-labeling; -labelling

UR - http://eudml.org/doc/270423

ER -

## References

top- [1] G. Chartrand, D. Erwin, D.W. VanderJagt and P. Zhang, γ-Labelings of graphs, Bull. Inst. Combin. Appl. 44 (2005) 51-68. Zbl1074.05079
- [2] J.A. Gallian, A dynamic survey of graph labeling, Electron. J. Combin. #DS6 (Oct. 2003 Version). Zbl0953.05067
- [3] S.M. Hegde, On (k,d)-graceful graphs, J. Combin. Inform. System Sci. 25 (2000) 255-265. Zbl1219.05165

## Citations in EuDML Documents

top## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.