Decompositions of Complete Graphs into Isomorphic Spanning Trees with Given Diameters

We use a new technique for decomposition of complete graphs with even number of vertices based on \( 2n \)-cyclic blended labeling to show that for every \( k > 1 \) odd, and every \( d \), \( 3 \leq d \leq 2^qk – 1 \), there exists a spanning tree of diameter \( d \) that factorizes \( K_{2^qk} \).