A (p,q) graph G with the p vertices and q edges is Mod(k) vertex magic for any integer k=2,l??Zk and there exists a injective map f from V(G) to { ?? 2 , ?? 2 + l, ?? 2 +l+1,... ?? 2 +k(p-1)} such that for any edge e, and the sum of the labels of vertices adjacent with the e are all equal to the same constant modulo k. In this paper, we prove that Generalized 2-complement some graphs namely S(K1,n), Spl (Cn) are Mod(k) vertex magic graphs.

—In this research paper, we proposed an ACO with a versatile for vector middle channel for the expulsion of motivation commotion from shading pictures. Regularly, the homogeneousness among the pixels is adulterated, when motivation clamor extraordinarily contorted the pictures. In the proposed method, just when the sifting activity will be done if the pixel is observed to be ruined. The choice about a specific pixel of being undermined or not relies upon the straight forecast blunder figured from the non-causal locale around the pixel under operation. Versatile window based vector middle separating activity will be done, if the mistake of the center pixel of the bit outperforms the officially characterized limit esteem. The span of versatile window will rely upon the level of blunder as indicated by the effectively characterized limit esteem. The proposed sifting system in charge of enhancing the pinnacle flag to clamor proportion (PSNR).

Let G (V, E) be a finite, non-trivial, simple and undirected graph of order n and size m. For an one to one assignment f: V(G)?{1,2,…., n}, A Quotient labeling f* : ?? ?? ? {1, 2, ..... , n} defined by ?? * (uv)= ? ? ? ? ? ? ( ) ( ) f v f u where f(u) > f(v), then the edge labels need not be distinct. The q-labeling number ql(f*) is the maximum value of f*(E(G)), and the Quotient Labeling Number QL(G) is the minimum amongql(f*). The bounds for the Quotient labeling number for corona ofsome ladder graphs likeclosed ladder,open ladder, slanting ladder, open triangular ladder, closed triangular ladder and diagonal ladder are found in this paper.

In the business world communitarian mind outline an extremely utilize full graph used to outwardly sort out data Visualizing. The Mind maps is an online electronic condition is an all the more effective approach to work together and upgrade cooperation, and the execution specifically when working from various areas and diverse circumstance. It is likewise an extremely extraordinary approach to introduce thoughts and ideas to potential clients. Online electronic personality mapping programming or desktop mind mapping programming with shared workspace and work bunches reconciliation furnishes clients with a cloud-based stage and devices which take into consideration multiuser altering continuously, making multi-provincial groups more compelling over the association.