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

P. Roushini Leely Pushpam; A. Saibulla

Discussiones Mathematicae Graph Theory (2012)

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

## Access Full Article

top## Abstract

top## How to cite

topP. 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

top- [1] M. Bača and C. Barrientos, Graceful and edge antimagic labelings, Ars Combin. 96 (2010) 505-513.
- [2] M. Bača, Y. Lin, M. Miller and R. Simanjuntak, New construction of magic and antimagic graph labeling, Util. Math. 60 (2001) 229-239. Zbl1011.05056
- [3] H. Enomoto, A.S. Llodo, T. Nakamigawa and G. Ringel, Super edge magic graphs, SUT J. Math. 34 (1998) 105-109. Zbl0918.05090
- [4] R.M. Figueroa-Centeno, R. Ichishima and F.A. Muntaner-Batle, The place of super edge magic labelings among other classes of labelings, Discrete Math. 231 (2001) 153-168, doi: 10.1016/S0012-365X(00)00314-9. Zbl0977.05120
- [5] J. Gallian, A dynamic survey of graph labeling, Electron. J. Combin. 17 (2010) #DS6. Zbl0953.05067
- [6] F. Harrary, Graph Theory ( Addison-Wesley, 1994).
- [7] N. Hartsfield and G. Ringel, Pearls in Graph Theory (Academic Press, Boston, San Diego, New York, London, 1990). Zbl0703.05001
- [8] S.M. Hegde and Sudhakar Shetty, On magic graphs, Australas. J. Combin. 27 (2003) 277-284.
- [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] 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] 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] K.A. Sugeng, M. Miller and M. Bača, Super edge antimagic total labelings, Util. Math. 71 (2006) 131-141.

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.