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Sequences on Graphs with Symmetries Linfan Mao Chinese Academy of Mathematics and System Science, Beijing, 10080, P.R.China Beijing Institute of Civil Engineering and Architecture, Beijing, 100044, P.R.China E-mail: [email protected]

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Page 1: Sequences on Graphs with Symmetriesfs.unm.edu/ScPr/SequencesOnGraphs.pdf · Walk. A walk of a graph G is an alternating sequence of vertices and edges for 1 < i < n. , en, With ei

Sequences on Graphs with Symmetries

Linfan MaoChinese Academy of Mathematics and System Science,

Beijing, 10080, P.R.ChinaBeijing Institute of Civil Engineering and Architecture,

Beijing, 100044, P.R.ChinaE-mail: [email protected]

Page 2: Sequences on Graphs with Symmetriesfs.unm.edu/ScPr/SequencesOnGraphs.pdf · Walk. A walk of a graph G is an alternating sequence of vertices and edges for 1 < i < n. , en, With ei

§1. Sequences

Page 3: Sequences on Graphs with Symmetriesfs.unm.edu/ScPr/SequencesOnGraphs.pdf · Walk. A walk of a graph G is an alternating sequence of vertices and edges for 1 < i < n. , en, With ei
Page 4: Sequences on Graphs with Symmetriesfs.unm.edu/ScPr/SequencesOnGraphs.pdf · Walk. A walk of a graph G is an alternating sequence of vertices and edges for 1 < i < n. , en, With ei
Page 5: Sequences on Graphs with Symmetriesfs.unm.edu/ScPr/SequencesOnGraphs.pdf · Walk. A walk of a graph G is an alternating sequence of vertices and edges for 1 < i < n. , en, With ei
Page 6: Sequences on Graphs with Symmetriesfs.unm.edu/ScPr/SequencesOnGraphs.pdf · Walk. A walk of a graph G is an alternating sequence of vertices and edges for 1 < i < n. , en, With ei
Page 7: Sequences on Graphs with Symmetriesfs.unm.edu/ScPr/SequencesOnGraphs.pdf · Walk. A walk of a graph G is an alternating sequence of vertices and edges for 1 < i < n. , en, With ei

§2. Graphs with Labelings

Page 8: Sequences on Graphs with Symmetriesfs.unm.edu/ScPr/SequencesOnGraphs.pdf · Walk. A walk of a graph G is an alternating sequence of vertices and edges for 1 < i < n. , en, With ei

Example

Page 9: Sequences on Graphs with Symmetriesfs.unm.edu/ScPr/SequencesOnGraphs.pdf · Walk. A walk of a graph G is an alternating sequence of vertices and edges for 1 < i < n. , en, With ei
Page 10: Sequences on Graphs with Symmetriesfs.unm.edu/ScPr/SequencesOnGraphs.pdf · Walk. A walk of a graph G is an alternating sequence of vertices and edges for 1 < i < n. , en, With ei
Page 11: Sequences on Graphs with Symmetriesfs.unm.edu/ScPr/SequencesOnGraphs.pdf · Walk. A walk of a graph G is an alternating sequence of vertices and edges for 1 < i < n. , en, With ei
Page 12: Sequences on Graphs with Symmetriesfs.unm.edu/ScPr/SequencesOnGraphs.pdf · Walk. A walk of a graph G is an alternating sequence of vertices and edges for 1 < i < n. , en, With ei
Page 13: Sequences on Graphs with Symmetriesfs.unm.edu/ScPr/SequencesOnGraphs.pdf · Walk. A walk of a graph G is an alternating sequence of vertices and edges for 1 < i < n. , en, With ei

Labeling.

Page 14: Sequences on Graphs with Symmetriesfs.unm.edu/ScPr/SequencesOnGraphs.pdf · Walk. A walk of a graph G is an alternating sequence of vertices and edges for 1 < i < n. , en, With ei
Page 15: Sequences on Graphs with Symmetriesfs.unm.edu/ScPr/SequencesOnGraphs.pdf · Walk. A walk of a graph G is an alternating sequence of vertices and edges for 1 < i < n. , en, With ei
Page 16: Sequences on Graphs with Symmetriesfs.unm.edu/ScPr/SequencesOnGraphs.pdf · Walk. A walk of a graph G is an alternating sequence of vertices and edges for 1 < i < n. , en, With ei

Smarandachely Labeling.

Page 17: Sequences on Graphs with Symmetriesfs.unm.edu/ScPr/SequencesOnGraphs.pdf · Walk. A walk of a graph G is an alternating sequence of vertices and edges for 1 < i < n. , en, With ei
Page 18: Sequences on Graphs with Symmetriesfs.unm.edu/ScPr/SequencesOnGraphs.pdf · Walk. A walk of a graph G is an alternating sequence of vertices and edges for 1 < i < n. , en, With ei
Page 19: Sequences on Graphs with Symmetriesfs.unm.edu/ScPr/SequencesOnGraphs.pdf · Walk. A walk of a graph G is an alternating sequence of vertices and edges for 1 < i < n. , en, With ei
Page 20: Sequences on Graphs with Symmetriesfs.unm.edu/ScPr/SequencesOnGraphs.pdf · Walk. A walk of a graph G is an alternating sequence of vertices and edges for 1 < i < n. , en, With ei
Page 21: Sequences on Graphs with Symmetriesfs.unm.edu/ScPr/SequencesOnGraphs.pdf · Walk. A walk of a graph G is an alternating sequence of vertices and edges for 1 < i < n. , en, With ei

§3. Smarandache Sequences on Symmetric Graphs

Page 22: Sequences on Graphs with Symmetriesfs.unm.edu/ScPr/SequencesOnGraphs.pdf · Walk. A walk of a graph G is an alternating sequence of vertices and edges for 1 < i < n. , en, With ei
Page 23: Sequences on Graphs with Symmetriesfs.unm.edu/ScPr/SequencesOnGraphs.pdf · Walk. A walk of a graph G is an alternating sequence of vertices and edges for 1 < i < n. , en, With ei
Page 24: Sequences on Graphs with Symmetriesfs.unm.edu/ScPr/SequencesOnGraphs.pdf · Walk. A walk of a graph G is an alternating sequence of vertices and edges for 1 < i < n. , en, With ei
Page 25: Sequences on Graphs with Symmetriesfs.unm.edu/ScPr/SequencesOnGraphs.pdf · Walk. A walk of a graph G is an alternating sequence of vertices and edges for 1 < i < n. , en, With ei
Page 26: Sequences on Graphs with Symmetriesfs.unm.edu/ScPr/SequencesOnGraphs.pdf · Walk. A walk of a graph G is an alternating sequence of vertices and edges for 1 < i < n. , en, With ei
Page 27: Sequences on Graphs with Symmetriesfs.unm.edu/ScPr/SequencesOnGraphs.pdf · Walk. A walk of a graph G is an alternating sequence of vertices and edges for 1 < i < n. , en, With ei
Page 28: Sequences on Graphs with Symmetriesfs.unm.edu/ScPr/SequencesOnGraphs.pdf · Walk. A walk of a graph G is an alternating sequence of vertices and edges for 1 < i < n. , en, With ei
Page 29: Sequences on Graphs with Symmetriesfs.unm.edu/ScPr/SequencesOnGraphs.pdf · Walk. A walk of a graph G is an alternating sequence of vertices and edges for 1 < i < n. , en, With ei

§4. Groups on Symmetric Graphs

Page 30: Sequences on Graphs with Symmetriesfs.unm.edu/ScPr/SequencesOnGraphs.pdf · Walk. A walk of a graph G is an alternating sequence of vertices and edges for 1 < i < n. , en, With ei
Page 31: Sequences on Graphs with Symmetriesfs.unm.edu/ScPr/SequencesOnGraphs.pdf · Walk. A walk of a graph G is an alternating sequence of vertices and edges for 1 < i < n. , en, With ei
Page 32: Sequences on Graphs with Symmetriesfs.unm.edu/ScPr/SequencesOnGraphs.pdf · Walk. A walk of a graph G is an alternating sequence of vertices and edges for 1 < i < n. , en, With ei
Page 33: Sequences on Graphs with Symmetriesfs.unm.edu/ScPr/SequencesOnGraphs.pdf · Walk. A walk of a graph G is an alternating sequence of vertices and edges for 1 < i < n. , en, With ei
Page 34: Sequences on Graphs with Symmetriesfs.unm.edu/ScPr/SequencesOnGraphs.pdf · Walk. A walk of a graph G is an alternating sequence of vertices and edges for 1 < i < n. , en, With ei

§5. Speculation

Page 35: Sequences on Graphs with Symmetriesfs.unm.edu/ScPr/SequencesOnGraphs.pdf · Walk. A walk of a graph G is an alternating sequence of vertices and edges for 1 < i < n. , en, With ei
Page 36: Sequences on Graphs with Symmetriesfs.unm.edu/ScPr/SequencesOnGraphs.pdf · Walk. A walk of a graph G is an alternating sequence of vertices and edges for 1 < i < n. , en, With ei
Page 37: Sequences on Graphs with Symmetriesfs.unm.edu/ScPr/SequencesOnGraphs.pdf · Walk. A walk of a graph G is an alternating sequence of vertices and edges for 1 < i < n. , en, With ei

In fact, it indeed means a combinatorial notion on mathematical objects following for researchers:

Page 38: Sequences on Graphs with Symmetriesfs.unm.edu/ScPr/SequencesOnGraphs.pdf · Walk. A walk of a graph G is an alternating sequence of vertices and edges for 1 < i < n. , en, With ei

Sincerely Thanks!


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