Zhongyuan Che

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The concept of a k-pairable graph was introduced by Chen (On k-pairable graphs, Discrete Mathematics 287 (2004), 11–15) as an extension of hypercubes and graphs with an antipodal isomorphism. In this talk, we introduce a special class of k-pairable graphs which are called uniquely pairable graphs. Then we give a characterization of uniquely pairable graphs(More)
Let k be a positive integer. A graph G is said to be k-pairable if its automorphism group contains an involution φ such that d(x, φ(x)) ≥ k for any vertex x of G. The pair length of a graph G, denoted as p(G), is the maximum k such that G is k-pairable; p(G) = 0 if G is not k-pairable for any positive integer k. Some new results have been obtained since(More)
The k-pairable graphs, introduced by Chen in 2004, constitute a wide class of graphs with a new type of symmetry, which includes many graphs of theoretical and practical importance, such as hypercubes, Hamming graphs of even order, antipodal graphs (also called diametrical graphs, or symmetrically even graphs), S-graphs, etc. Let k be a positive integer. A(More)
A labeling f : V (G) → {1, 2, . . . , d} of the vertex set of a graph G is said to be proper d-distinguishing if it is a proper coloring of G and any nontrivial automorphism of G maps at least one vertex to a vertex with a different label. The distinguishing chromatic number of G, denoted by χD(G), is the minimum d such that G has a proper d-distinguishing(More)
The concepts of k-pairable graphs and the pair length of a graph were introduced by Chen [Discrete Math. 287 (2004), 11–15] to generalize an elegant result of Graham et al. [Amer. Math. Monthly 101 (1994), 664– 667] from hypercubes and graphs with antipodal isomorphisms to a much larger class of graphs. A graph G is k-pairable if there is a positive integer(More)
Let denote the class of connected plane bipartite graphs with no pendant edges. A finite face s of a graphG ∈ is said to be a forcing face ofG if the subgraph ofG obtained by deleting all vertices of s together with their incident edges has exactly one perfect matching. This is a natural generalization of the concept of forcing hexagons in a hexagonal(More)
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