Non-Coprime Graph of Integers

N. Mohamed Rilwan; M. Mohamed Sameema; A. Roobin Oli

doi:https://doi.org/10.14445/22315373/IJMTT-V66I2P513

International Journal of Mathematics Trends and Technology

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Volume 66 | Issue 2 | Year 2020 | Article Id. IJMTT-V66I2P513 | DOI : https://doi.org/10.14445/22315373/IJMTT-V66I2P513

Non-Coprime Graph of Integers

N. Mohamed Rilwan, M. Mohamed Sameema, A. Roobin Oli

Abstract

In this paper, we introduce a new concept of graph named as non-coprime graph of integers. A non-coprime graph of integers, denoted by Γ(n), is arrived from an integer set X = { 1,2......,n} whereas the vertex set V(G) =X\Y where Y = { x : gcd(x,y) = 1 for every y ε X } and the edge set E(G) = {(x,y) : x,y,ε X and gcd(x,y) ≠ 1 }. In this paper, we analyzed some basic properties of the non-coprime graph of integers such as circumference, girth, clique, chromatic number and also prove that the bounds of the domination number, independence number and independent domination number is sharp.

Keywords

non-coprime graph, domination, Hamiltonian cycle, semi perfect

References

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Citation :

N. Mohamed Rilwan, M. Mohamed Sameema, A. Roobin Oli, "Non-Coprime Graph of Integers," International Journal of Mathematics Trends and Technology (IJMTT), vol. 66, no. 2, pp. 116-120, 2020. Crossref, https://doi.org/10.14445/22315373/IJMTT-V66I2P513