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

Let G x 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 P,.+l x P,+1, and each component of each of CA x Pn+l, Pm+l x (7, and Cm x C, 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 X P,+I, P,.+l X C, and C,. × C. is edge-decomposable into cycles of uniform length ms, where s is a suitable divisor of n, (c) C2i+1 × C2j+l is factorizable into shortest odd cycles, (d) each component C4i x C4j is factorizable into four-cycles, and (e) each component of Cmx C4j admits of a bi-pancyclic ordering. AMS Classification: 05C38; 05C45; 05C70