2011/03/16 by Mohsen Jannesari, Jannesari, Mohsen, Behnaz Omoomi +1 · 1 citation
Computer Science · Mathematics · #05C12 #05C15 #05C20 #05C90 #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems #Graph theory and applications
paper · pdf · doi:10.48550/arxiv.1103.3169
openalex publication_date 2011/03/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For an ordered set W=\w1,w2,...,wk\ of vertices and a vertex v in a connected graph G, the ordered k-vector r(v|W):=(d(v,w1),d(v,w2),...,d(v,wk)) 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. A resolving set for G with minimum cardinality is called a basis of G and its cardinality is the metric dimension of G. A connected graph G is called randomly k-dimensional graph if each k-set of vertices of G is a basis of G. In this paper, we study randomly k-dimensional graphs and provide some properties of these graphs.