On γ-labelings of trees
Gary Chartrand ; David Erwin ; Donald W. VanderJagt ; Ping Zhang
Discussiones Mathematicae Graph Theory, Tome 25 (2005), p. 363-383 / Harvested from The Polish Digital Mathematics Library
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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)=Σe∈E(G)f'K(e). The maximum value of a γ-labeling of G is defined as valmax(G)=maxval(f):fisaγ-labelingofG; while the minimum value of a γ-labeling of G is valmin(G)=minval(f):fisaγ-labelingofG; The values valmax(Sp,q) and valmin(Sp,q) are determined for double stars Sp,q. We present characterizations of connected graphs G of order n for which valmin(G)=n or valmin(G)=n+1.

Publié le : 2005-01-01
EUDML-ID : urn:eudml:doc:270423 
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Gary Chartrand; David Erwin; Donald W. VanderJagt; Ping Zhang. On γ-labelings of trees. Discussiones Mathematicae Graph Theory, Tome 25 (2005) pp. 363-383. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgt_1289/

[000] [1] G. Chartrand, D. Erwin, D.W. VanderJagt and P. Zhang, γ-Labelings of graphs, Bull. Inst. Combin. Appl. 44 (2005) 51-68. | Zbl 1074.05079

[001] [2] J.A. Gallian, A dynamic survey of graph labeling, Electron. J. Combin. #DS6 (Oct. 2003 Version). | Zbl 0953.05067

[002] [3] S.M. Hegde, On (k,d)-graceful graphs, J. Combin. Inform. System Sci. 25 (2000) 255-265. | Zbl 1219.05165