The Sparing Number of the Cartesian Product of Certain Graphs

K. P. Chithra, K. A. Germina, N. K. Sudev

Abstract


Let $\mathbb{N}_0$ be the set of all non-negative integers. An integer additive set-indexer (IASI) is defined as an injective function $f:V(G)\rightarrow \mathcal{P}(\mathbb{N}_0)$ such that the induced function $f^+:E(G) \rightarrow \mathcal{P}(\mathbb{N}_0)$ defined by $f^+ (uv) = f(u)+ f(v)$ is also injective, where $f(u)+f(v)$ is the sumset of $f(u)$ and $f(v)$ and $\mathcal{P}(\mathbb{N}_0)$ is the power set of $\mathbb{N}_0$. If $f^+(uv)=k~\forall~uv\in E(G)$, then $f$ is said to be a $k$-uniform integer additive set-indexer. An integer additive set-indexer $f$ is said to be a weak integer additive set-indexer if $|f^+(uv)|=max(|f(u)|,|f(v)|)~\forall ~ uv\in E(G)$. In this paper, we study about the sparing number of the cartesian product of two graphs

Keywords


Integer additive set-indexers, mono-indexed elements of a graphs, weak integer additive set-indexers, sparing number of a graph

Full Text:

PDF

References


B. D. Acharya (1983), Set-Valuations and Their Applications, MRI Lecture

notes in Applied Mathematics, The Mehta Research Institute of Mathematics and Mathematical Physics, New Delhi.

J. A. Bondy and U. S. R. Murty (2008), Graph Theory, Springer.

J. A. Gallian (2011). A Dynamic Survey of Graph Labelling, The Electronic Journal of Combinatorics (DS 16).

K. A. Germina and T. M. K. Anandavally (2012). Integer Additive Set-Indexers of a Graph: Sum Square Graphs, Journal of Combinatorics, Information and System Sciences, 37(2-4), 345-358.

K. A. Germina and N. K. Sudev (2013). On Weakly Uniform Integer Additive Set-Indexers of Graphs, Int. Math. Forum, 8(37), 1827-1834.

G. Hahn and C. Tardif (1997). Graph Homomorphism: Structure and Symmetries in Graph Symmetry: Algebraic Methods and Applications (Eds: G Hahn and G Sabidussi), Kluwer Acad. Pub., 107-166.

R. Hammack, W. Imrich and S. Klavzar (2011). Handbook of Product graphs, CRC

Press.

F. Harary (1994). Graph Theory, Addison-Wesley Publishing Company Inc.

W. Imrich and S. Klavzar (2000). Product Graphs: Structure and Recognition, Wiley.

W. Imrich, S. Klavzar and D. F. Rall (2008). Topics in Graph Theory: Graphs and Their Cartesian Products, A K Peters.

N. K. Sudev and K. A. Germina (2014). A Characterisation of Weak Integer Additive Set-Indexers of Graphs, ISPACS J. Fuzzy Set Valued Analysis, 2014, Article Id: jfsva-0189, 7 pages.

N. K. Sudev and K. A. Germina (2014). Weak Integer Additive Set-Indexers of Graph Operations, Global J. Math. Sciences: Theory and Practical, 6(1),25-36.

N. K. Sudev and K. A. Germina (2014). A Note on Sparing Number of Graphs, to

appear in Adv. and Applns. of Disc. Math.

N. K. Sudev and K. A. Germina (2014). Weak integer Additive Set-Indexers of

Graph Certain Products, submitted.

D. B. West (2001). Introduction to Graph Theory, Pearson Education Inc.


Refbacks

  • »


eISSN 0975-8607; pISSN 0976-5905