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Let (Γ, *) be a finite group and e be its identity. Let A be a generating set of Γ such that e / ∈ A and a −1 ∈ A for all a ∈ A. Then the Cayley graph is defined by G = (V (G), E(G)), where V (G) = Γ and E(G) = {(x, x * a) |x ∈ V (G), a ∈ A}, denoted by Cay(Γ, A). Circulant graphs are special case of Cayley graphs when Γ = (Z n , ⊕ n), where ⊕ n is the operation addition modulo n. In this paper, for the Circulant graphs Cir(n, A), where A = {1, 2,. .. k, n − 1, n − 2,. .. , n − k} and k ≤ n−1 2 , the connected domination number has been obtained.

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Clustering spatial data is a well-known problem that has been extensively studied. Grouping similar data in large 2-dimensional spaces to find hidden patterns or meaningful sub-groups has many applications such as satellite imagery, geographic information systems, medical image analysis, marketing, computer visions, etc. Spatial clustering has been an active research area in Spatial Data Mining (SDM). Many methods on spatial clustering have been proposed in the literature, but few of them have taken into account constraints that may be present in the data clustering. In this paper, we discuss the problem of spatial clustering with obstacles constraints and propose a novel spatial clustering using edge detection method and K-Mediods, which objective is to cluster the spatial data (images) with the constraints and also comparing the result with the various constraints based clustering algorithms in terms of number of clusters and its execution time.The Edge detection based K-Mediods algorithms can not only given attention to higher speed and stronger global optimum search, but also get down to the obstacles and facilitator constraints and practicalities of spatial clustering. Taking into account these constraints during the clustering process is costly and the modeling of the constraints is paramount for good performance. The results on real datasets shown that the Edge detection based spatial clustering with the constraints are performs better than the existing constraint based clustering.