Multi-Decomposition of Product Graphs into Kites and Stars on Four Edges - Velusamy, Jothimani; Palanisamy, Hemalatha (IndoMS, 2025)
A decomposition of a graph G is a set of edge-disjoint subgraphs H_1,H_2,...,H_r of G such that every edge of G belongs to exactly one H_i. If all the subgraphs in the decomposition of G are isomorphic to a graph H then we say that G is H-decomposable. The graph G has an {H_1^α,H_2^β}-decomposition, if α copies of H_1 and β copies of H_2 decompose G, where α and β are non-negative integers. In this paper, we have obtained the decomposition of K_m × K_n into α kites and β stars on four edges for some of the admissible pairs (α,β), whenever mn(m-1)(n-1) 0(mod 8), for m ≥ 3 and n ≥ 4. Also, we have obtained the decomposition of K_m K_n into α kites and β stars on four edges for some of the admissible pairs (α,β), whenever m(m-1)n^2 0(mod 8), for m ≥ 3 and n ≥ 4. Here K_m × K_n and K_m K_n respectively denotes the tensor and wreath product of complete graphs.