Let G = (V (G),E(G)) be a simple graph and H be a subgraph of G. G admits an H-covering, if every edge in E(G) belongs to at least one subgraph of G that is isomorphic to H. An (a, d)-H-antimagic total labeling of G is a bijection λ: V (G) ∪ E(G) → {1, 2, 3, . . . , |V (G)| + |E(G)|} such that for all subgraphs H′ isomorphic to H, the H′ weights [...] constitute an arithmetic progression a, a+d, a+2d, . . . , a+(n−1)d where a and d are positive integers and n is the number of subgraphs of G isomorphic to H. Additionally, the labeling λ is called a super (a, d)-H-antimagic total labeling if λ(V (G)) = {1, 2, 3, . . . , |V (G)|}. In this paper we study super (a, d)-H-antimagic total labelings of star related graphs Gu[Sn] and caterpillars.
@article{bwmeta1.element.doi-10_7151_dmgt_1832,
author = {K.M. Kathiresan and S. David Laurence},
title = {On Super (a, d)-H-Antimagic Total Covering of Star Related Graphs},
journal = {Discussiones Mathematicae Graph Theory},
volume = {35},
year = {2015},
pages = {755-764},
zbl = {1327.05297},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_7151_dmgt_1832}
}
K.M. Kathiresan; S. David Laurence. On Super (a, d)-H-Antimagic Total Covering of Star Related Graphs. Discussiones Mathematicae Graph Theory, Tome 35 (2015) pp. 755-764. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_7151_dmgt_1832/
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