Kronecker products of paths and cycles: Decomposition, factorization and bi-pancyclicity Original Research Article

Let G × H denote the Kronecker product of graphs G and H. Principal results are as follows: (a) If m is even and n ≡ 0 (mod 4), then one component of Pm+1 × Pn+1, and each component of each of Cm × Pn+1, Pm+1 × Cn and Cm × Cn are edge decomposable into cycles of uniform length rs, where r and s are suitable divisors of m and n, respectively, (b) if m and n are both even, then each component of each of Cm × Pn+1, Pm+1 × Cn and Cm × Cn is edge-decomposable into cycles of uniform length ms, where s is a suitable divisor of n, (c) C2i+1 × C2j+1 is factorizable into shortest odd cycles, (d) each component C4i × C4j is factorizable into four-cycles, and (e) each component of Cm × C4j admits of a bi-pancyclic ordering.