Super (a,d)-edge antimagic total labeling of some classes of graphs

P. Roushini Leely Pushpam; A. Saibulla

doi:10.55937/sut/1343931268

January 2012 Super

(a,d)

-edge antimagic total labeling of some classes of graphs

P. Roushini Leely Pushpam, A. Saibulla

Author Affiliations +

SUT J. Math. 48(1): 1-12 (January 2012). DOI: 10.55937/sut/1343931268

Abstract

A graph $G(V,E)$ is $(a,d)$ -edge antimagic total if there exists a bijection $f:V(G) \cup E(G) \to \left\{ {1,2, \ldots \left| {V(G)} \right| + \left| {E(G)} \right|} \right\}$ such that the edge-weights ${\rm{\Lambda }}(uv) = f(u) + f(uv) + f(v),uv \in E(G)$ 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 f $(V(G)) = \left\{ {1,2, \ldots ,\left| {V(G)} \right|} \right\}$ . In this paper, we have obtained a relation between a super $(a,0)$ -edge antimagic total labeling and a super $(a,2)$ - edge antimagic total labeling of any graph. Also we study the super $(a,d)$ -edge antimagic total labeling of fan graphs and two special classes of star graphs namely bi-star and extended bi-star.

Acknowledgement

The authors are grateful to the anonymous referees whose comments helped a lot to improve the presentation of this paper.

Citation

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P. Roushini Leely Pushpam. A. Saibulla. "Super $(a,d)$ -edge antimagic total labeling of some classes of graphs." SUT J. Math. 48 (1) 1 - 12, January 2012. https://doi.org/10.55937/sut/1343931268