﻿ The 2-dimension of a Tree

# The 2-dimension of a Tree

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چکیده

Let \$x\$ and \$y\$ be two distinct vertices in a connected graph \$G\$. The \$x,y\$-location of a vertex \$w\$ is the ordered pair of distances from \$w\$ to \$x\$ and \$y\$, that is, the ordered pair \$(d(x,w), d(y,w))\$. A set of vertices \$W\$ in \$G\$ is \$x,y\$-located if any two vertices in \$W\$ have distinct \$x,y\$-location.A set \$W\$ of vertices in \$G\$ is 2-located if it is \$x,y\$-located, for some distinct vertices \$x\$ and \$y\$. The 2-dimension of \$G\$ is the order of a largest set that is 2-located in \$G\$. Note that this notion is related to the metric dimension of a graph, but not identical to it.We study in depth the trees \$T\$ that have a 2-locating set, that is, have 2-dimension equal to the order of \$T\$. Using these results, we have a nice characterization of the 2-dimension of arbitrary trees.

جستجوی کلمه کلیدی

resolvability
location number
2-dimension
tree
2-locating set برای دسترسی به متن کامل این مقاله و 10 میلیون مقاله دیگر ابتدا ثبت نام کنید

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