Large-scale low-Earth-orbit satellite constellations offer a promising platform for global low-latency networking, aided by faster propagation in free space than in fiber and copper. In such systems, end-to-end latency is largely determined by the inter-satellite link (ISL) topology. In particular, the network diameter, the maximum shortest path between any pair of satellites, serves as a key performance metric for time-sensitive applications. Designing diameter-optimal topologies is challenging due to degree constraints, line-of-sight limitations, and orbital dynamics. This paper proposes a two-stage optimization framework for ISL topology design. First, a continuous relaxation of the link selection problem is formulated as a convex program that maximizes the algebraic connectivity of the Laplacian, serving as a tractable surrogate for diameter minimization. Second, the resulting fractional solution is mapped to a feasible discrete topology using integer linear programming. An iterative local-search heuristic is also developed as a baseline. Extensive simulations on Walker-Delta constellations show that the proposed method consistently achieves smaller network diameters and improved robustness compared to conventional heuristics, while allowing trade-offs between latency and link persistence. The approach offers a principled framework for designing high-performance satellite mesh networks. For a constellation of 1,500 satellites, each equipped with four ISLs of up to 2,500 km, the network diameter can be reduced to as low as 12, yielding end-to-end delays under 90 ms between any two points on Earth.

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