# 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

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topK.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 -

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