On Super (a, d)-H-Antimagic Total Covering of Star Related Graphs

K.M. Kathiresan; S. David Laurence

Discussiones Mathematicae Graph Theory (2015)

  • Volume: 35, Issue: 4, page 755-764
  • ISSN: 2083-5892

Abstract

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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.

How to cite

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K.M. Kathiresan, and S. David Laurence. "On Super (a, d)-H-Antimagic Total Covering of Star Related Graphs." Discussiones Mathematicae Graph Theory 35.4 (2015): 755-764. <http://eudml.org/doc/276026>.

@article{K2015,
abstract = {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.},
author = {K.M. Kathiresan, S. David Laurence},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {super (a; d)-H-antimagic total labeling; star; super --antimagic total labeling},
language = {eng},
number = {4},
pages = {755-764},
title = {On Super (a, d)-H-Antimagic Total Covering of Star Related Graphs},
url = {http://eudml.org/doc/276026},
volume = {35},
year = {2015},
}

TY - JOUR
AU - K.M. Kathiresan
AU - S. David Laurence
TI - On Super (a, d)-H-Antimagic Total Covering of Star Related Graphs
JO - Discussiones Mathematicae Graph Theory
PY - 2015
VL - 35
IS - 4
SP - 755
EP - 764
AB - 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.
LA - eng
KW - super (a; d)-H-antimagic total labeling; star; super --antimagic total labeling
UR - http://eudml.org/doc/276026
ER -

References

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  5. [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[Crossref] Zbl0213.26203
  6. [6] A. Llado and J. Moragas, Cycle-magic graphs, Discrete Math. 307 (2007) 2925-2933. doi:10.1016/j.disc.2007.03.007[Crossref] Zbl1127.05090
  7. [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. Zbl1171.05045
  8. [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 [Crossref] 

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