Some Metrical Properties of Lattice Graphs of Finite Groups

Jia-Bao Liu, Mobeen Munir, Qurat-ul-Ain Munir and Abdul Rauf Nizami
Additional contact information
Jia-Bao Liu: School of Mathematics and Physics, Anhui Jianzhu University, Hefei 230601, 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

Mathematics, 2019, vol. 7, issue 5, 1-11

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.

Keywords: finite group; lattice graph; convex polytope; diameter; girth (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/7/5/398/pdf (application/pdf)
https://www.mdpi.com/2227-7390/7/5/398/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:7:y:2019:i:5:p:398-:d:227924

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().