Minimal doubly resolving sets of prism graphs

Abstract In this paper, we consider the problem of determining the minimal cardinality of double resolving sets for prism graphs . It is proved that the minimal cardinality is equal to four if is even and equal to three if is odd.

[1]  N. Duncan Leaves on trees , 2014 .

[2]  Jozef Kratica,et al.  Computing minimal doubly resolving sets of graphs , 2009, Comput. Oper. Res..

[3]  David R. Wood,et al.  On the Metric Dimension of Cartesian Products of Graphs , 2005, SIAM J. Discret. Math..

[4]  Jozef Kratica,et al.  Computing the metric dimension of graphs by genetic algorithms , 2009, Comput. Optim. Appl..

[5]  H. Coxeter Self-dual configurations and regular graphs , 1950 .

[6]  Nael B. Abu-Ghazaleh,et al.  Virtual Coordinate Backtracking for Void Traversal in Geographic Routing , 2005, ArXiv.

[7]  Thomas Erlebach,et al.  Network Discovery and Verification , 2005, IEEE Journal on Selected Areas in Communications.

[8]  Azriel Rosenfeld,et al.  Landmarks in Graphs , 1996, Discret. Appl. Math..