Independent graph of the finite group
T. Chalapathi, R. V M S S Kiran Kumar
TL;DR
This paper introduces the independent graph of the finite group Zn, where vertices are elements of Zn and edges connect elements with different orders, exploring its properties and structure.
Contribution
It defines and studies the independent graph of Zn, a new graph model based on element independence in finite groups.
Findings
Characterization of the independent graph IG(Zn)
Properties of independence in the graph
Structural insights into IG(Zn)
Abstract
Let a and b be any two elements in the group Zn of integers modulo n. Then a and b are called independent if O(a) not equal to O(b) . In this paper, we introduce and study independent graph of the group Zn, denoted by IG(Zn), is undirected simple graph whose vertex set is Zn and two distinct vertices a and b are adjacent in IG(Zn) if and only if a and b are independent in Zn.
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Taxonomy
TopicsFinite Group Theory Research · Coding theory and cryptography · graph theory and CDMA systems