2018/11/14 by Zubair Ahmad, Muhammad Ahmad, Ahmad, Z. +5 · 1 citation
Computer Science · Engineering · #Graph Labeling and Dimension Problems #graph theory and CDMA systems #Digital Image Processing Techniques
paper · pdf · doi:10.48550/arxiv.1811.05973
Let G be a connected graph and d(a,b) be the distance between the vertices a and b. A subset U =\u1,u2,⋯,uk\ of the vertices is called a resolving set for G if for every two distinct vertices a,b ∈ V(G), there is a vertex uξ∈ U such that d(a,uξ)≠ d(b,uξ). A resolving set containing a minimum number of vertices is called a metric basis for G and the number of vertices in a metric basis is its metric dimension denoted by dim(G). A resolving set U for G is fault-tolerant if U ∖ \u\ is also a resolving set, for each u ∈ U, and the fault-tolerant metric dimension of G is the minimum cardinality of such a set. In this paper we introduce the study of the fault-tolerant metric dimension of P(n,2) with prism graph.