Device-to-Device (i.e. D2D) communication technology not only magnify system capacity but also utilizes the gain of physical proximity of communicating devices to support services like proximity services, traffic offloading etc. from eNB (i.e. evolved Node-B). D2D communication enhanced resource efficiency and brought down traffic load from eNB in LTE-A networks. Coexistence of D2D users and conventional cellular users in the network, efficient resource sharing among devices becomes challenging task. The optimized resource allocation problem is NP-hard problem. To maximize total utility and resource efficiency of devices, we use interference graph model to estimate interference scenario among devices in cellular LTE-A networks. In this model devices present vertices whereas edges are formed among interfering devices. Further, we apply graph coloring based model to solve resource allocation problem in D2D communication underlaying cellular LTE-A networks. Moreover, the proposed algorithmic model gives better result than greedy orthogonal resource assignment scheme as well as achieve approaching performance with respect to optimal resource assignment schem, in an efficient resource allocation technique with feasible complexity of O(K.N ⁴ ), here K is the total number of RBs whereas N is number of devices in the cellular LTE-A networks.