Mathematics – Combinatorics
Scientific paper
2012-02-26
Mathematics
Combinatorics
9 pages, accepted by Ars Combinatoria on May 13, 2010
Scientific paper
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) = {(g_i,h_s)(g_j,h_t): g_ig_j belongs to E(G) and h_sh_t belongs to E(H)}. We prove that the direct product M_m(G) X M_n(H) of the generalized Mycielskians of G and H is a cover graph if and only if G or H is bipartite.
Lai Hsin-Hao
Lih Ko-Wei
Lin Chen-Ying
Tong Li-Da
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