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<p>&nbsp;In this paper, Digital image processing refers processing of two dimensional picture by a digital computer. Digital image is composed of a finite number of elements are called picture elements or pixels. These image are generally degraded by noise. Noise occurs during image capture, transmission or processing. Some of these noises are salt and pepper noise, gaussian noise and uniform noise. These noises can be removed by two kinds of filters either linear or nonlinear filters. The nonlinear filters which we use for filtering operation are median, midpoint and trimmed. The aim of the paper is to remove the pepper noise by using median filter and also there is possibility to change image matrix value in to connected graph and find the dominating set and dominating number for the image matrix value for better result with help of dominating technique in graph theory. The equivalent two dimensional matrix representation having picture for the image is generated using MATLAB- programming and the program for median filter process are simulated using VHDL and in this paper we try to include the dominating methods in image processing. In the graph theory, domanatin set a for a connected graph G = (V, E) is a subset S of V such that every vertex not in S is adjacent to at least one vertices of S . The domination number y(G) is the number of vertices in a dominating set of G.</p>