Cognitive radio network (CRN) is proposed to resolve the issue of the rare of available radio spectrum sources by introducing new concept of Channel assignment methods based on Dynamic spectrum allocation (DSA) algorithm, which can assign unused channel by PUs that can be allowed to recruit out with another user (the available spectrum to the SUs), So Cognitive radio technology is considered to be an efficient solution to improve the spectrum utilization efficiency of available spectrum resources and ensuring user fairness by considering choosing and using the "free spectrum" in reasonably manner. On this paper, we will introduce a novel methodology for spectrum allocation algorithm based on the graph-coloring theory. Unlike some already existed allocation algorithms based on CSGC , our algorithm will consider the B.w matching degree between SUs B.w requirements and it's available channels B.w, the interference degree between SUs represented by tolerable values not limited to binary values as used in previous algorithms and choose the channel with efficient impact on spectrum resources allocation process . Our goal here is the enhancement and improves of the total spectrum reward by meeting SUs B.w requirements, improve SUs satisfaction rate and reduce the required running time for allocation process as much as feasible to achieve a fast channel assignment with low complexity and computational time to satisfied the special need required for a real time application especially A/G Communication. Our simulation results show the feasibility of our proposed algorithms with graph and equation that indicates improvement in total spectrum reward, the satisfaction rate of SUs and reduction in algorithms running time overhead.