# CSASC 2013

9-13 June 2013
Koper, Slovenia
UTC timezone
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# Some Results for Roman-Domination Number of Cardinal Product of Paths and Cycles

Presented by Prof. Antoaneta KLOBUCAR
Type: Poster
Track: Poster Session

## Content

\begin{abstract} 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}.\\ In this paper we determine the lower and the upper bound for $\gamma_R(P_m\times P_n)$ as well as the exact value of $\displaystyle{\lim_{m,n\to \infty}\frac{P_m\times P_n}{mn}}$ where $P_m\times P_n$ stands for the cardinal product of two paths. We also generalize some results concerning cardinal product of two cycles $C_m\times C_n$. \end{abstract}

## Place

Location: Koper, Slovenia

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