Hamiltonian properties of lexicographic products
Jakub Teska

Abstract

The lexicographic product G[H] of two graphs G and H is obtained from G 
by replacing each vertex with a copy of H and adding all edges between 
any pair of copies corresponding to adjacent vertices of G. We 
generalize the lexicographic product such that we replace each vertex of 
G with arbitrary graph on the same number of vertices. We present 
sufficient and necessary conditions for traceability, hamiltonicity and 
hamiltonian connectivity of G[H] if G is a path.