TY - JOUR
AU - Suhadi Wido Saputro
AU - Andrea Semanicova-Fenovc
AU - Martin Baca
AU - Marcela Lascsakova
PY - 2018/02/27
Y2 - 2024/10/16
TI - On fractional metric dimension of comb product graphs
JF - Statistics, Optimization & Information Computing
JA - Stat., optim. inf. comput.
VL - 6
IS - 1
SE - Research Articles
DO - 10.19139/soic.v6i1.473
UR - http://www.iapress.org/index.php/soic/article/view/soic.20180310
AB - A vertex $z$ in a connected graph $G$ \textit{resolves} two vertices $u$ and $v$ in $G$ if $d_G(u,z)
eq d_G(v,z)$. \ A set of vertices $R_G\{u,v\}$ is a set of all resolving vertices of $u$ and $v$ in $G$. \ For every two distinct vertices $u$ and $v$ in $G$, a \textit{resolving function} $f$ of $G$ is a real function $f:V(G)\rightarrow[0,1]$ such that $f(R_G\{u,v\})\geq1$. \ The minimum value of $f(V(G))$ from all resolving functions $f$ of $G$ is called the \textit{fractional metric dimension} of $G$. \ In this paper, we consider a graph which is obtained by the comb product between two connected graphs $G$ and $H$, denoted by $G\rhd_o H$. \ For any connected graphs $G$, we determine the fractional metric dimension of $G\rhd_o H$ where $H$ is a connected graph having a stem or a major vertex.
ER -