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Simultaneous Resolvability in Families of Corona Product Graphs | | Yunior Ramírez-Cruz
; Alejandro Estrada-Moreno
; Juan A. Rodríguez-Velázquez
; | | Date: |
18 Jun 2015 | | Abstract: | Let ${cal G}$ be a graph family defined on a common vertex set $V$ and let
$d$ be a distance defined on every graph $Gin {cal G}$. A set $Ssubset V$ is
said to be a simultaneous metric generator for ${cal G}$ if for every $Gin
{cal G}$ and every pair of different vertices $u,vin V$ there exists $sin S$
such that $d(s,u)
e d(s,v)$. The simultaneous metric dimension of ${cal G}$
is the smallest integer $k$ such that there is a simultaneous metric generator
for ${cal G}$ of cardinality $k$. We study the simultaneous metric dimension
of families composed by corona product graphs. Specifically, we focus on the
case of two particular distances defined on every $Gin {cal G}$, namely, the
geodesic distance $d_G$ and the distance $d_{G,2}:V imes V
ightarrow
mathbb{N}cup {0}$ defined as $d_{G,2}(x,y)=min{d_{G}(x,y),2}$. | | Source: | arXiv, 1506.5667 | | Services: | Forum | Review | PDF | Favorites | |
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