The Sierpiński graph S(n, Km), known for its recursive and hierarchical construction, serves as a significant model for multiprocessor interconnection architectures. Its extended variant, denoted S+ (n, Km), further strengthens these properties and has practical relevance in areas such as parallel computation and VLSI circuit design. This work investigates the unresolved Maximum Subgraph Problem (MSP) for the extended Sierpiński graph S+ (n, Km), with n ≥ 2, a problem originally proposed by Joshwa et al. [1], and still open for general values of m. We introduce a computational framework, implemented in SageMath, for determining the maximal edge count among all subgraphs induced by r vertices, where 1 ≤ r ≤ 3n + 1. In addition, we examine minimum wirelength embeddings of S+ (n, Km) into various hierarchical graph topologies, a key factor in optimizing communication efficiency and layout complexity in networked systems.