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International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

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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[9] E. Saias, “Etude du graphe divisorie”I, Periodica Math. Hung., to appear.
[10] Wayne Goddard and Michael A. Henning, “Independent domination in graphs: A survey and recent results”, Discrete Mathematics 313 (2013) 839-854.
[11] Farzaneh Mansoori, Ahmad Erfanian, and Behnaz Tolue, Non-coprime graph of a finite group, AIP Conf. Proc. 1750, 050017-1 – 050017-9, 21 June 2016.

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

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