In this paper, we focus on the existence of symmetric λ-configurations with λ = 2, 3, and 4. Three new spatial configurations (v 8 ) 2 for v = 30, 31, and 32 are constructed. The existence of a spatial configuration (v k ) 2 are updated for k 10. The existence tables for symmetric λ-configurations for λ = 3, 4, and small k are also given.
A decomposition of Kn(g)∖L, the complete n‐partite equipartite graph with a subgraph L (called the leave) removed, into edge disjoint copies of a graph G is called a maximum group divisible packing of Knfalse(gfalse) with G if L contains as few edges as possible. We examine all possible minimum leaves for maximum group divisible (K4−e)‐packings. Necessary and sufficient conditions are established for their existences.
Nuclear design could be used for constructing packing and covering of a graph in combinatorial design theory. We generalize the nuclear design to group divisible nuclear design, and discuss the upper bound of block number for group divisible nuclear design with block size 4.
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