# On super (a,d)-edge antimagic total labeling of certain families of graphs

• Volume: 32, Issue: 3, page 535-543
• ISSN: 2083-5892

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## Abstract

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A (p, q)-graph G is (a,d)-edge antimagic total if there exists a bijection f: V(G) ∪ E(G) → {1, 2,...,p + q} such that the edge weights Λ(uv) = f(u) + f(uv) + f(v), uv ∈ E(G) form an arithmetic progression with first term a and common difference d. It is said to be a super (a, d)-edge antimagic total if the vertex labels are {1, 2,..., p} and the edge labels are {p + 1, p + 2,...,p + q}. In this paper, we study the super (a,d)-edge antimagic total labeling of special classes of graphs derived from copies of generalized ladder, fan, generalized prism and web graph.

## How to cite

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P. Roushini Leely Pushpam, and A. Saibulla. "On super (a,d)-edge antimagic total labeling of certain families of graphs." Discussiones Mathematicae Graph Theory 32.3 (2012): 535-543. <http://eudml.org/doc/270793>.

@article{P2012,
abstract = {A (p, q)-graph G is (a,d)-edge antimagic total if there exists a bijection f: V(G) ∪ E(G) → \{1, 2,...,p + q\} such that the edge weights Λ(uv) = f(u) + f(uv) + f(v), uv ∈ E(G) form an arithmetic progression with first term a and common difference d. It is said to be a super (a, d)-edge antimagic total if the vertex labels are \{1, 2,..., p\} and the edge labels are \{p + 1, p + 2,...,p + q\}. In this paper, we study the super (a,d)-edge antimagic total labeling of special classes of graphs derived from copies of generalized ladder, fan, generalized prism and web graph.},
author = {P. Roushini Leely Pushpam, A. Saibulla},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {edge weight; magic labeling; antimagic labeling; ladder; fan graph; prism and web graph},
language = {eng},
number = {3},
pages = {535-543},
title = {On super (a,d)-edge antimagic total labeling of certain families of graphs},
url = {http://eudml.org/doc/270793},
volume = {32},
year = {2012},
}

TY - JOUR
AU - P. Roushini Leely Pushpam
AU - A. Saibulla
TI - On super (a,d)-edge antimagic total labeling of certain families of graphs
JO - Discussiones Mathematicae Graph Theory
PY - 2012
VL - 32
IS - 3
SP - 535
EP - 543
AB - A (p, q)-graph G is (a,d)-edge antimagic total if there exists a bijection f: V(G) ∪ E(G) → {1, 2,...,p + q} such that the edge weights Λ(uv) = f(u) + f(uv) + f(v), uv ∈ E(G) form an arithmetic progression with first term a and common difference d. It is said to be a super (a, d)-edge antimagic total if the vertex labels are {1, 2,..., p} and the edge labels are {p + 1, p + 2,...,p + q}. In this paper, we study the super (a,d)-edge antimagic total labeling of special classes of graphs derived from copies of generalized ladder, fan, generalized prism and web graph.
LA - eng
KW - edge weight; magic labeling; antimagic labeling; ladder; fan graph; prism and web graph
UR - http://eudml.org/doc/270793
ER -

## References

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9. [9] A. Kotzig and A. Rosa, Magic valuation of finite graphs, Canad. Math. Bull. 13 (1970) 451-461, doi: 10.4153/CMB-1970-084-1. Zbl0213.26203
10. [10] R. Simanjuntak, F. Bertault and M. Miller, Two new (a, d)-antimagic graph labelings, Proc. Eleventh Australian Workshop Combin. Algor., Hunrer Valley, Australia (2000) 179-189.
11. [11] K.A. Sugeng and M. Miller, Relationship between adjacency matrices and super (a, d)-edge antimagic total labelings of graphs, J. Combin. Math. Combin. Comput. 55 (2005) 71-82. Zbl1100.05087
12. [12] K.A. Sugeng, M. Miller and M. Bača, Super edge antimagic total labelings, Util. Math. 71 (2006) 131-141.

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