On Metric Dimension of Circulant Graph Cn(1, 2) Joining n-paths

Let H = H(V, E) be a graph. A subset of vertices M in V (H) is said to be are solving set (or metric generator) for H if every y, z is an element of V (H) with y not equal z, there existsa vertex a is an element of M such that d (a, y) not equal d(a, z). A metric generator containing a minimum number of vertices is called a metric basis for Hand the cardinality of this metric basis is the metric dimension of H, denoted by d(m)(i)(H). Let C-n(q)(1,2) be a graph obtained from the circulant graph Cn(1,2) by joining n-paths of length q at each vertex of the graph C-n(1,2). In this work, we show that the metric dimension of the graph C-n(q)(1,2)is three when n equivalent to 0,2,3mod(4) and four whenn equivalent to 1mod(4).