Metric dimension of fullerene graphs
oleh: Shehnaz Akhter, Rashid Farooq
| Format: | Article |
|---|---|
| Diterbitkan: | Indonesian Combinatorial Society (InaCombS); Graph Theory and Applications (GTA) Research Centre; University of Newcastle, Australia; Institut Teknologi Bandung (ITB), Indonesia 2019-04-01 |
Deskripsi
<p>A resolving set <span class="math"><em>W</em></span> is a set of vertices of a graph <span class="math"><em>G</em>(<em>V</em>, <em>E</em>)</span> such that for every pair of distinct vertices <span class="math"><em>u</em>, <em>v</em> ∈ <em>V</em>(<em>G</em>)</span>, there exists a vertex <span class="math"><em>w</em> ∈ <em>W</em></span> satisfying <span class="math"><em>d</em>(<em>u</em>, <em>w</em>) ≠ <em>d</em>(<em>v</em>, <em>w</em>)</span>. A resolving set with minimum number of vertices is called metric basis of <span class="math"><em>G</em></span>. The metric dimension of <span class="math"><em>G</em></span>, denoted by <span class="math">dim(<em>G</em>)</span>, is the minimum cardinality of a resolving set of <span class="math"><em>G</em></span>. In this paper, we consider <span class="math">(3, 6)</span>-fullerene and <span class="math">(4, 6)</span>-fullerene graphs and compute the metric dimension for these fullerene graphs. We also give conjecture on the metric dimension of <span class="math">(3, 6)</span>-fullerene and <span class="math">(4, 6)</span>-fullerene graphs.</p>