In this paper, we define asymptotic dimension of fuzzy metric spaces in the sense George and Veeramini. We prove that is an invariant coarse category spaces. also show several consequences setting which resemble setting. finish with calculating a few

This paper presents two complementary approaches to comparing the shape and topology of solid models. First, we develop a mapping of solid models toModel SignatureGraphs (MSGs)— labeled, undirected graphs that abstract the boundary representation of the model and capture relevant shape and engineering attributes. Model Signature Graphs are then used to de ne metric spaces over arbitrary sets of...

Using the two-way distance, we introduce concept of weak metric dimension a strongly connected digraph [Formula: see text]. We first establish lower and upper bounds for number arcs in text] by using diameter text], characterize all digraphs attaining or bound. Then study with 1 classify vertex-transitive having 1. Finally, order n are determined.

In the localization game on a graph, goal is to find fixed but unknown target node $v^\star$ with least number of distance queries possible. $j^{th}$ step game, player single $v_j$ and receives, as an answer their query, between nodes $v^\star$. The sequential metric dimension (SMD) minimal that needs guess absolute certainty, no matter where is. term SMD originates from related notion (MD), wh...

Characterization of singular graphs can be reduced to the non-trivial solutions of a system of linear homogeneous equations Ax = 0 for the 0-1 adjacency matrix A. A graph G is singular of nullity η(G) ≥ 1, if the dimension of the nullspace ker(A) of its adjacency matrix A is η(G). Necessary and sufficient conditions are determined for a graph to be singular in terms of admissible induced subgra...

Abstract A resolving set for a graph $$\Gamma $$ ? is collection of vertices S , chosen so that each vertex v the list distances from to members uniquely specifies . The metric dimension $$\mu (\Gamma )$$ ? ( ) smallest size We consider...