Large-scale low-Earth-orbit satellite constellations offer a promising platform for global low-latency networking, in part because signals propagate faster 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 longest shortest path, in hops, between any pair of satellites--serves as a key performance metric for time-sensitive applications. Designing diameter-optimal topologies is challenging due to node degree constraints, orbital dynamics, and the combinatorial nature of link selection. 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 graph Laplacian, serving as a tractable surrogate for diameter minimization. Second, the resulting fractional solution is mapped to a feasible topology via maximum-weight b-matching, a problem solvable in polynomial time. Simulations on Walker-Delta constellations show that the proposed method consistently achieves smaller network diameters than a local-search baseline and standard patterned topologies. For a 1,584-satellite constellation in which each satellite has four ISLs of up to 2,500 km, the diameter is as small as 12 hops, and the maximum propagation delay between any two satellites is about 90 ms. With up- and downlinks adding up to 8 ms, the user-to-user propagation delay is at most about 98 ms, comparable to the delay over a great-circle fiber route between antipodal points on Earth.

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