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Some Metrical Properties of Lattice Graphs of Finite Groups

Author

Listed:
  • Jia-Bao Liu

    (School of Mathematics and Physics, Anhui Jianzhu University, Hefei 230601, China
    School of Mathematics, Southeast University, Nanjing 210096, China)

  • Mobeen Munir

    (Department of Mathematics, Division of Science and Technology, University of Education, Lahore 54000, Pakistan)

  • Qurat-ul-Ain Munir

    (Department of Mathematics, COMSATS University Islamabad, Lahore Campus 54000, Pakistan)

  • Abdul Rauf Nizami

    (Faculty of Information Technology, University of Central Punjab, Lahore 54000, Pakistan)

Abstract

This paper is concerned with the combinatorial facts of the lattice graphs of Z p 1 × p 2 × ⋯ × p m , Z p 1 m 1 × p 2 m 2 , and Z p 1 m 1 × p 2 m 2 × p 3 1 . We show that the lattice graph of Z p 1 × p 2 × ⋯ × p m is realizable as a convex polytope. We also show that the diameter of the lattice graph of Z p 1 m 1 × p 2 m 2 × ⋯ × p r m r is ∑ i = 1 r m i and its girth is 4.

Suggested Citation

  • Jia-Bao Liu & Mobeen Munir & Qurat-ul-Ain Munir & Abdul Rauf Nizami, 2019. "Some Metrical Properties of Lattice Graphs of Finite Groups," Mathematics, MDPI, vol. 7(5), pages 1-11, May.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:5:p:398-:d:227924
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