1. bookVolume 41 (2021): Issue 2 (November 2021)
Journal Details
License
Format
Journal
eISSN
2084-0373
First Published
16 Apr 2017
Publication timeframe
2 times per year
Languages
English
access type Open Access

On Order Prime Divisor Graphs of Finite Groups

Published Online: 06 Sep 2021
Volume & Issue: Volume 41 (2021) - Issue 2 (November 2021)
Page range: 419 - 437
Received: 03 Jul 2019
Accepted: 01 Nov 2020
Journal Details
License
Format
Journal
eISSN
2084-0373
First Published
16 Apr 2017
Publication timeframe
2 times per year
Languages
English
Abstract

The order prime divisor graph 𝒫𝒟(G) of a finite group G is a simple graph whose vertex set is G and two vertices a, bG are adjacent if and only if either ab = e or o(ab) is some prime number, where e is the identity element of the group G and o(x) denotes the order of an element xG. In this paper, we establish the necessary and sufficient condition for the completeness of order prime divisor graph 𝒫𝒟(G) of a group G. Concentrating on the graph 𝒫𝒟(Dn), we investigate several properties like degrees, girth, regularity, Eulerianity, Hamiltonicity, planarity etc. We characterize some graph theoretic properties of 𝒫𝒟 (ℤn), 𝒫𝒟 (Sn), 𝒫𝒟 (An).

Keywords

MSC 2010

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