Displaying similar documents to “On the dimer problem and the Ising problem in finite 3-dimensional lattices.”

Existence of perfect matchings in a plane bipartite graph

Zhongyuan Che (2010)

Czechoslovak Mathematical Journal

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We give a necessary and sufficient condition for the existence of perfect matchings in a plane bipartite graph in terms of elementary edge-cut, which extends the result for the existence of perfect matchings in a hexagonal system given in the paper of F. Zhang, R. Chen and X. Guo (1985).

Deficiency of forests

Sana Javed, Mujtaba Hussain, Ayesha Riasat, Salma Kanwal, Mariam Imtiaz, M. O. Ahmad (2017)

Open Mathematics

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An edge-magic total labeling of an (n,m)-graph G = (V,E) is a one to one map λ from V(G) ∪ E(G) onto the integers {1,2,…,n + m} with the property that there exists an integer constant c such that λ(x) + λ(y) + λ(xy) = c for any xy ∈ E(G). It is called super edge-magic total labeling if λ (V(G)) = {1,2,…,n}. Furthermore, if G has no super edge-magic total labeling, then the minimum number of vertices added to G to have a super edge-magic total labeling, called super edge-magic deficiency...