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A lexicographic product of graphs  G  and  H , denoted byis defined as a graph with the vertex setand an edgepresents in the product wheneveror ( u1  =  u2  and). We investigate the sufficient conditions for vertex pancyclicity of lexicographic products of complete graphs  K n, paths  P nor cycles  C nwith a general graph. We obtain that (i) if  G1  is a traceable graph of even order and  G2  is a graph with at least one edge, thenis vertex pancyclic; (ii) if  G1  is hamiltonian and  G2  is a graph with at least one edge, thenis vertex pancyclic.

Vertex pancyclicity over lexicographic products