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- Zhongyuan Che
- Discrete Mathematics
- 2008

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)

- Zhongyuan Che, Zhibo Chen
- Discrete Mathematics
- 2010

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)

- Zhongyuan Che, Zhibo Chen
- Australasian J. Combinatorics
- 2015

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)

- Zhongyuan Che, Karen L. Collins
- Journal of Graph Theory
- 2007

- Zhongyuan Che, Karen L. Collins
- Electr. J. Comb.
- 2013

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)

Let G be a connected graph with odd girth 2k + 1. Then G is a (2k + 1)-angulated graph if every two vertices of G are joined by a path such that each edge of the path is in some (2k + 1)-cycle. We prove that if G is (2k+1)-angulated, and H is connected with odd girth at least 2k+3, then any retract R of the box (or Cartesian) product G2H is isomorphic to… (More)

- Zhongyuan Che, Karen L. Collins, Claude Tardif
- Journal of Graph Theory
- 2008

- Zhongyuan Che, Zhibo Chen
- Australasian J. Combinatorics
- 2016

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)

- Zhongyuan Che, Zhibo Chen
- Discrete Applied Mathematics
- 2013

- Zhongyuan Che, Zhibo Chen
- Discrete Mathematics
- 2008

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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