Weak Integer Additive Set-Indexers of Certain Graph Products

N. K. Sudev, K. A. Germina

Abstract


Let $\matbb{N}_0$ be the set of all non-negative integers and $\mathcal{P}(\mathbb{N}_0)$ be its power set. An integer additive set-indexer (IASI) is dened as an injective function $f:V(G)\to \mathcal{P}(\mathbb{N}_0)$ such that the induced function $f^+:E(G)\to \mathcal{P}(\mathbb{N}_0)$ defined by $f^+(uv) = f(u) + f(v)$ is also injective, where $f(u) + f(v)$ is the sumset of $f(u)$ and $f(v)$. An IASI f is said to be a weak IASI if $|f^+(uv)| = \max(|f(u)|,|f(v)|)$ $\forall$ $uv \in E(G)$. In this paper, we study the admissibility of weak IASI by certain graph products of two weak IASI graphs.


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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.

G. Chartrand and P. Zhang (2005), Introduction to Graph Theory, McGraw-Hill Inc.

N. Deo (1974), Graph Theory with Applications to Engineering and Computer Science, PHI Learning.

R. Frucht and F. Harary (1970), On the Corona of Two Graphs, Aequationes Math., 4(3), 322-325.

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.

C D Godsil and B D McKay, (1978). A New Graph Product and its Spectrum,

Bull. Austral. Mat. Soc., 18, 21-28.

G Hahn and G Sabidussi, (1997). Graph Symmetry: Algebraic Methods and

Applications, NATO Adv. Sci. Inst. Ser. 497, Springer.

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, S Klavzar, (2000). Product Graphs: Structure and Recogni-

tion, 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). Weak Integer Additive Set-Indexers of

Certain Graph Structures, Annals of Pure and Appl. Math., 6(2),140-149.

M Tavkoli, F Rhbarnia and A R Ashra, (2013). Note on Strong Product of

Graphs, Kragujevac J. Math., 37(1), 187193.

P M Weichsel, (1962). The Kronecker Product of Graphs, Proc of the Amer.

Math. Soc. 13(1): 4752, doi:10.2307/2033769.

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




DOI: http://dx.doi.org/10.26713%2Fjims.v6i1.236

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