Distance-regular graphs are a highly symmetric form of graph, whose connectivity patterns are based equally on distance, and are used both in theory and practice. The structural properties of distance-regular graphs discussed in this paper include the conditions of symmetry, intersection arrays, and their relationship to strongly regular graphs. It also talks about the distance-regular methods of algebraic constructions and graph operations. In order to enhance secure communication networks, it is proposed to use a hybrid scheme, which is a combination of graph-theoretic frameworks and the existing encryption schemes. The proposed method has been experimentally shown to increase the network robustness by 21.6 and structural attack vulnerability by 18.3 compared to traditional topologies. The findings depict how distance-regular graphs can be applicable in the formation of robust, scalable and secure communication frameworks in next generation distributed systems.