Applicable Analysis and Discrete Mathematics | |
ON THE METRIC DIMENSION AND FRACTIONAL METRIC DIMENSION OF THE HIERARCHICAL PRODUCT OF GRAPHS | |
article | |
Min Feng1  Kaishun Wang1  | |
[1] School of Mathematical Sciences, Laboratory of Mathematics and Complex Systems, Beijing Normal University | |
关键词: Resolving set; metric dimension; resolving function; fractional metric dimension; hierarchical product; binomial tree; | |
DOI : 10.2298/AADM130521009F | |
学科分类:社会科学、人文和艺术(综合) | |
来源: Univerzitet u Beogradu * Elektrotehnicki Fakultet / University of Belgrade, Faculty of Electrical Engineering | |
【 摘 要 】
A set of vertices W resolves a graph G if every vertex of G is uniquely determined by its vector of distances to the vertices in W. The metric dimensionfor G, denoted by dim(G), is the minimum cardinality of a resolving set of G.In order to study the metric dimension for the hierarchical product Gu22 ⊓Gu11of two rooted graphs Gu22 and Gu11, we first introduce a new parameter, therooted metric dimension rdim(Gu11) for a rooted graph Gu11. If G1 is not a pathwith an end-vertex u1, we show that dim(Gu22 ⊓ Gu11) = |V (G2)| · rdim(Gu11),where |V (G2)| is the order of G2. If G1 is a path with an end-vertex u1,we obtain some tight inequalities for dim(Gu22 ⊓ Gu11). Finally, we show thatsimilar results hold for the fractional metric dimension.
【 授权许可】
Unknown
【 预 览 】
Files | Size | Format | View |
---|---|---|---|
RO202307080003575ZK.pdf | 241KB | download |