The Metric Dimension of Lexicographic Product of Graphs

Details The Metric Dimension of Lexicographic Product of Graphs The Metric Dimension of Lexicographic Product of Graphs

2011-03-17

arxiv.org/abs/1103.3336v1

Mathematics

Combinatorics

11 pages

Scientific paper

For an ordered set $W=\{w_1,w_2,...,w_k\}$ of vertices and a vertex $v$ in a connected graph $G$, the ordered $k$-vector $r(v|W):=(d(v,w_1),d(v,w_2),...,d(v,w_k))$ is called the (metric) representation of $v$ with respect to $W$, where $d(x,y)$ is the distance between the vertices $x$ and $y$. The set $W$ is called a resolving set for $G$ if distinct vertices of $G$ have distinct representations with respect to $W$. The minimum cardinality of a resolving set for $G$ is its metric dimension. In this paper, we study the metric dimension of the lexicographic product of graphs $G$ and $H$, $G[H]$. First, we introduce a new parameter which is called adjacency metric dimension of a graph. Then, we obtain the metric dimension of $G[H]$ in terms of the order of $G$ and the adjacency metric dimension of $H$.

Affiliated with

Also associated with

No associations

Rating

The Metric Dimension of Lexicographic Product of Graphs does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with The Metric Dimension of Lexicographic Product of Graphs, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and The Metric Dimension of Lexicographic Product of Graphs will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-247468