# Computers in Scientific Discovery 6

21-25 August 2012
Portorož, Slovenia
UTC timezone
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# LOWER AND UPPER BOUND FOR ROMAN DOMINATION NUMBER ON CARDINAL PRODUCT OF PATHS

Presented by Ivona PULJIć
Type: Poster

## Content

For a graph $G=(V,E)$, \emph{a Roman dominating function} (RDF) is a function $f \colon V \to \{0,1,2\}$ satisfying the condition that every vertex $u$ for which $f(u)=0$ is adjacent to at least one vertex $v$ for which $f(v)=2$. The weight of an RDF equals $w(f)=\sum_{v\in V}f(v)=|V_1|+2|V_2|$. An RDF for which $w(f)$ achieves its minimum is called \emph{a} $\gamma_R$\emph{-function} and its weight, denoted by $\gamma_R(G)$, is called \emph{a Roman domination number}.\\ We studied the Roman domination on cardinal product of two paths $P_m \times P_n$ and determined the lower and the upper bound for $\gamma_R(P_m\times P_n)$ as well as the exact value of $\displaystyle{\lim_{m,n\to \infty}\frac{P_m\times P_n}{mn}}$.

## Place

Location: Portorož, Slovenia
Address: University of Primorska, Faculty of Tourism Studies, Obala 11a, SI-6320 Portorož - Portorose, Slovenia
Room: VP1

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