Authors : G.C. Basavaraju, M. Vishukumar and P. Raghunath
Abstract: Let G = (V, E) be a graph. A set S⊆V is called resolving set if for every u, v∈V there exist w∈V such that d(u, w) ≠ = d(v, w). The resolving set with minimum cardinality is called metric basis and its cardinality is called metric dimention and it is denoted by β(G). A set D⊆V is called dominating set if every vertex not in D is adjacent to at least one vertex in D. The dominating set with minimum cardinality is called domination number of G and it is denoted by γ(G). A set which is both resolving set as well as dominating set is called metro dominating set. The minimum cardinality of a metro dominating set is called metro domination number of G and it is denoted by γβ(G). In this study we determine on the metro domination number of cartesian product of Pm Pn and Cm Cn .
G.C. Basavaraju, M. Vishukumar and P. Raghunath, 2019. On the Metro Domination Number of Cartesian Product of Pm_Pn and Cm_Cn. Journal of Engineering and Applied Sciences, 14: 114-119.