Geodesic
On Super $(a, d)$-$H$-Antimagic Total Covering of Star Related Graphs
Discussiones Mathematicae. Graph Theory, Tome 35 (2015) no. 4, pp. 755-764.

Voir la notice de l'article provenant de la source Library of Science

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 wt(H^') = ∑_v ∈ V (H^') λ (v) + ∑_e ∈ E(H^')λ (e)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 G_u[S_n] and caterpillars.
Keywords: super (a, d)-H-antimagic total labeling, star 
@article{DMGT_2015_35_4_a11,
     author = {Kathiresan, K.M. and Laurence, S. David},
     title = {On {Super} $(a, d)$-$H${-Antimagic} {Total} {Covering} of {Star} {Related} {Graphs}},
     journal = {Discussiones Mathematicae. Graph Theory},
     pages = {755--764},
     publisher = {mathdoc},
     volume = {35},
     number = {4},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGT_2015_35_4_a11/}
}
TY  - JOUR
AU  - Kathiresan, K.M.
AU  - Laurence, S. David
TI  - On Super $(a, d)$-$H$-Antimagic Total Covering of Star Related Graphs
JO  - Discussiones Mathematicae. Graph Theory
PY  - 2015
SP  - 755
EP  - 764
VL  - 35
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DMGT_2015_35_4_a11/
LA  - en
ID  - DMGT_2015_35_4_a11
ER  - 
%0 Journal Article
%A Kathiresan, K.M.
%A Laurence, S. David
%T On Super $(a, d)$-$H$-Antimagic Total Covering of Star Related Graphs
%J Discussiones Mathematicae. Graph Theory
%D 2015
%P 755-764
%V 35
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DMGT_2015_35_4_a11/
%G en
%F DMGT_2015_35_4_a11
Kathiresan, K.M.; Laurence, S. David. On Super $(a, d)$-$H$-Antimagic Total Covering of Star Related Graphs. Discussiones Mathematicae. Graph Theory, Tome 35 (2015) no. 4, pp. 755-764. http://geodesic.mathdoc.fr/item/DMGT_2015_35_4_a11/

[1] A. Gutierrez and A. Lladó, Magic coverings, J. Combin. Math. Combin. Comput. 55 (2005) 43-56.

[2] N. Inayah, A.N.M. Solmankl and R. Simanjuntak, On (a, d)-H-antimagic coverings of graphs, J. Combin. Math. Combin. Comput. 71 (2009) 273-281.

[3] N. Inayah, A. Llado and J. Moragas, Magic and antimagic H-decompositions, Dis- crete Math. 312 (2012) 1367-1371. doi:10.1016/j.disc.2011.11.041

[4] N. Inayah, R. Simanjuntak and A.N.M. Salman, Super (a, d)-H-antimagic total labelings for shackles of a connected graph H, Australas. J. Combin. 57 (2013) 127-138.

[5] A. Kotzig and A. Rosa, Magic valuations of finite graph, Canad. Math. Bull. 13 (1970) 451-461. doi:10.4153/CMB-1970-084-1

[6] A. Llado and J. Moragas, Cycle-magic graphs, Discrete Math. 307 (2007) 2925-2933. doi:10.1016/j.disc.2007.03.007

[7] T.K. Maryati, E.T. Baskoro and A.N.M. Salman, Ph-supermagic labelings some trees, J. Combin. Math. Combin. Comput. 65 (2008) 197-204.

[8] M. Roswitha and E.T. Baskoro, H-magic covering on some classes of graphs, AIP Conf. Proc. 1450 (2012) 135-138. doi:10.1063/1.4724129