Let G be a connected graph with vertex set V(G) and d(u,v) the distance between vertices u v. A of S={s1,s2,…,sk}?V(G) is called resolving for if, any two distinct u,v?V(G), there si?S such that d(u,si)?d(v,si). S fault-tolerant if S\{x} also set, each x in S, metric dimension G, denoted by ??(G), minimum cardinality set. The paper Basak et al. on circulant graphs Cn(1,2,3) has determined exact...

For an ordered subset S = { v 1 , …, k } of vertices in a connected graph G and edge e ′ the metric -representation ′= b is vector r ( ′| )=( d ′, ),…, )) where i )=min{ ), )} . A dominant generator for vertex cover such that edges have pairwise different -representations. smallest size called basis The denoted by D m ) dimension. In this paper, concept dimension (DEMD short) introduced its bas...

The concepts of entropy and dimension as applied to dynamical systems are reviewed from a physical point of view. The information dimension, which measures the rate at which the information contained in a probability density scales with resolution, fills a logical gap in the classification of attractors in terms of metric entropy, fractal dimension, and topological entropy. Several examples are...