Web1 de mar. de 2007 · In this work the exact values of the dimension of graph G are calculated for some important families of graphs: the complete graphs, the bipartite complete … Web1 de abr. de 2013 · A (di)graph G is (strongly) connected if for any two distinct vertices u and v of G, there exists a path from u to v. In this paper we only consider finite strongly …

Metric dimension (graph theory) - Wikipedia

WebOur purpose in this note is to present a natural geometrical definition of the dimension of a graph and to explore some of its ramifications. In §1 we determine the dimension of some special graphs. We observe in §2 that several results in the literature are unified by the … Web1 de jan. de 2002 · The metric dimension of graph obtained from a graph operation also has been studied such as Cartesian product graphs [5,8,14], join product graphs [3,4,26], corona product graphs ... how did topaz form

[2001.09168] The Threshold Dimension of a Graph - arXiv.org

WebCorollary 2.4. A tree T of order n ≥ 4 is (2, t)-metric dimensional if and only if T contains a support vertex which is adjacent to at least two leaves. An example of a (2, t)-metric dimensional tree is the star graph K1,n−1 , whose (2, t)-metric dimension is dim2,t (K1,n−1 ) = n−1. WebIn this context, we propose a fuzzy lowdimensional representation by mapping any given graph onto a k-dimensional space such that the distance between any two nodes determines their adjacency status. The proposed mapping utilizes an intersection graph representation where k-dimensional balls represent the nodes, and the likelihood of … Web26 de jul. de 2005 · A set S of vertices in a graph G resolves G if every vertex is uniquely determined by its vector of distances to the vertices in S. The metric dimension of G is the minimum cardinality of a resolving set of G. This paper studies the metric dimension of cartesian products G*H. We prove that the metric dimension of G*G is tied in a strong … how did tony sly die