A STUDY OF AN UNDIRECTED GRAPH ON A FINITE SUBSET OF NATURAL NUMBERS

Ivy Chakrabarty; Joseph Varghese Kureethara; Mukti Acharya

doi:10.56827/SEAJMMS.2022.1803.35

Ivy Chakrabarty Department of Mathematics, Christ University, Hosur Road, Bengaluru - 560029, INDIA
Joseph Varghese Kureethara Department of Mathematics, Christ University, Hosur Road, Bengaluru - 560029, INDIA
Mukti Acharya Department of Mathematics, Christ University, Hosur Road, Bengaluru - 560029, INDIA

DOI: https://doi.org/10.56827/SEAJMMS.2022.1803.35

Abstract

Let $G_{n}=(V,E)$ be an undirected simple graph, whose vertex set comprises of the natural numbers which are less than $n$ but not relatively prime to $n$ and two distinct vertices $u,v \in V$ are adjacent if and only if $\gcd(u,v)>1$. Connectedness, completeness, minimum degree, maximum degree, independence number, domination number and Eulerian property of the graph $G_n$ are studied in this paper.