When is the Direct Product of Generalized Mycielskians a Cover Graph?
Abstract
A graph is said to be a cover graph if it is the underlying graph of the Hasse diagram of a finite partially ordered set. The direct product G X H of graphs G and H is the graph having vertex set V(G) X V(H) and edge set E(G X H) = (gi,hs)(gj,ht): gigj belongs to E(G) and hsht belongs to E(H). We prove that the direct product Mm(G) X Mn(H) of the generalized Mycielskians of G and H is a cover graph if and only if G or H is bipartite.
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