On (a,d) - 1-Vertex- Antimagic Labeled Graphs

Beena S

doi:https://doi.org/10.14445/22315373/IJMTT-V65I4P504

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 65 | Issue 4 | Year 2019 | Article Id. IJMTT-V65I4P504 | DOI : https://doi.org/10.14445/22315373/IJMTT-V65I4P504

On (a,d) - 1-Vertex- Antimagic Labeled Graphs

Beena S

Abstract

Let G be a graph onp – vertices. Then a vertex labeling f : V (G )  {1,2,..., p} is called (a , d )  1 – vertex antimagic - vertex (1-VAV) labeling of G , if the vertex weight induced by f at each vertex of V are a , a  d , a  2 d ,..., a  ( p  1)d where a and d are some fixed positive integers. In this work, we have proved every graph is an induced subgraph of a regular (a , d )  1 – VA graph and some of its properties.

Keywords

(a,d)-1, VAV labeling, ∑' labeling, regular graph.

References

[1] S Beena, ‘On ∑ & ∑ labeled graphs’ Discrete Mathematics 309(2009) 1783 – 1787.
[2] K R Parthasarathy, ‘Basic Graph Theory, Tata Mc.Graw – Hill (1994).
[3] D B West, Introduction to Graph Theory’, (2nd Edn) Pearson Education (2001).

Citation :

Beena S, "On (a,d) - 1-Vertex- Antimagic Labeled Graphs," International Journal of Mathematics Trends and Technology (IJMTT), vol. 65, no. 4, pp. 19-21, 2019. Crossref, https://doi.org/10.14445/22315373/IJMTT-V65I4P504