Weak Integer Additive SetIndexers of Certain Graph Operations
Abstract
An integer additive setindexer is defined as an injective function $f:V(G)\rightarrow 2^{\mathbb{N}_0}$ such that the induced function $g_f:E(G) \rightarrow 2^{\mathbb{N}_0}$ defined by $g_f (uv) = f(u)+ f(v)$ is also injective, where $f(u)+f(v)$ is the sum set of $f(u)$ and $f(v)$ and $\mathbb{N}_0$ is the set of all nonnegative integers. If $g_f(uv)=k \forall uv\in E(G)$, then $f$ is said to be a $k$uniform integer additive setindexers. An integer additive setindexer $f$ is said to be a weak integer additive setindexer if $g_f(uv)=max(f(u),f(v)) \forall uv\in E(G)$. A weak integer additive setindexer $f$ is called a weakly $k$uniform integer additive setindexer if $g_f(e)=k \forall e\in E(G)$. We have some characteristics of the graphs which admit weak and weakly uniform integer additive setindexers. In this paper, we study the admissibility of weak integer additive setindexer by certain graphs and finite graph operations.
 Publication:

arXiv eprints
 Pub Date:
 October 2013
 arXiv:
 arXiv:1310.6091
 Bibcode:
 2013arXiv1310.6091S
 Keywords:

 Mathematics  Combinatorics;
 05C78
 EPrint:
 10 pages, submitted, arXiv admin note: text overlap with arXiv:1310.5779