Biography
Dr. Yilun Shang
Dr. Yilun Shang
Northumbria University, UK
Title: Fault-Tolerant Metric Dimension of Circulant Graphs
Abstract: 

Let G be a connected graph with vertex set V(G) and d(u,v) be the distance between the vertices u and v. A set of vertices S={s1,s2,…,sk} ⊂ V(G) is called a resolving set for G if, for any two distinct vertices u,v∈V(G), there is a vertex si∈S such that d(u,si)≠d(v,si). A resolving set S for G is fault-tolerant if S\{x} is also a resolving set, for each x in S, and the fault-tolerant metric dimension of G, denoted by β′(G), is the minimum cardinality of such a set. The paper of Basak et al. on fault-tolerant metric dimension of circulant graphs Cn(1,2,3) has determined the exact value of β′(Cn(1,2,3)). In this presentation, we present the extension of the results of Basak et al. to the graph Cn(1,2,3,4) and the exact value of β′(Cn(1,2,3,4)) for all n≥22. 

Biography: 

Dr. Yilun Shang received his BS and PhD degrees in Mathematics from Shanghai Jiao Tong University. He received his PGCert with Commendation in Academic Practice from Northumbria University. He is an Associate Professor with Northumbria University. His research interests mainly include complex networks, system science, applied probability, algebra and combinatorics. He is a recipient of Dimitrie Pompeiu Prize, Energies Best Paper Award, and Outstanding Associate Editor Award of IEEE Access. He is an Editor-in-Chief for Research in Mathematics.