Roman domination number of Generalized Petersen Graphs P(n,2)
A $Roman\ domination\ function$ on a graph $G=(V, E)$ is a function $f:V(G)\rightarrow\{0,1,2\}$ satisfying the condition that every vertex $u$ with $f(u)=0$ is adjacent to at least one vertex $v$ with $f(v)=2$. The $weight$ of a Roman domination function $f$ is the value $f(V(G))=\sum_{u\in V(G)}f(...
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Main Authors | , , , |
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Format | Journal Article |
Language | English |
Published |
11.03.2011
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Subjects | |
Online Access | Get full text |
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Summary: | A $Roman\ domination\ function$ on a graph $G=(V, E)$ is a function
$f:V(G)\rightarrow\{0,1,2\}$ satisfying the condition that every vertex $u$
with $f(u)=0$ is adjacent to at least one vertex $v$ with $f(v)=2$. The
$weight$ of a Roman domination function $f$ is the value $f(V(G))=\sum_{u\in
V(G)}f(u)$. The minimum weight of a Roman dominating function on a graph $G$ is
called the $Roman\ domination\ number$ of $G$, denoted by $\gamma_{R}(G)$. In
this paper, we study the {\it Roman domination number} of generalized Petersen
graphs P(n,2) and prove that $\gamma_R(P(n,2)) = \lceil {\frac{8n}{7}}\rceil (n
\geq 5)$. |
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DOI: | 10.48550/arxiv.1103.2419 |