Among interconnection topologies, the hypercube is both popular and highly attractive, extensively used in parallel computing and network design due to its versatility and scalability. Its desirable properties have inspired the development of several variants, including the folded hypercube, crossed cube, augmented cube, locally twisted cube, enhanced hypercube, twisted cube, extended hypercube, Mobius cube, and Fibonacci cube, each improving specific aspects such as fault tolerance, communication efficiency, and scalability. A generalized hypercube Qn (S), where S ⊆ {1, 2, …, n}, is an extension of the classic hypercube graph. It has a vertex set {0, 1}n, and edges are formed between vertices whose Hamming distance belongs to the set S. This structure allows for flexible modeling of relationships and connectivity, making it a valuable tool in parallel computing, network design, and combinatorial optimization. This paper focuses on the generalized structure of the hiked hypercube when S = {1, 2, …, j} ⊆ {1, 2, …, n}, and addresses the maximum subgraph problem. Additionally, we determine the minimum linear arrangement of this topology using graph embedding techniques, highlighting its potential in optimizing interconnection networks.