G.C. Basavaraju, P. Raghunath, M. Vishukumar,
On the Metro Domination Number of Cartesian Product of Pm_Pn and Cm_Cn,
Journal of Engineering and Applied Sciences,
Volume 14,Issue 1,
2019,
Pages 114-119,
ISSN 1816-949x,
jeasci.2019.114.119,
(https://makhillpublications.co/view-article.php?doi=jeasci.2019.114.119)
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 .
Keywords: cardinality;metro dominating set;dominating set;landmark;Metric dimension;product