Original Research Article

Article volume = 2021 and issue = 1

Pages: 67–83

Article publication Date: November, 1, 2021

You can download PDF file of the article here: Download

Visited 122 times and downloaded 77 times

# On K-Dprime Divisor Function Graph

#### John Rafael M. Antalan, Jerwin G. De Leon, Regine P. Dominguez

Department of Mathematics and Physics, College of Science, Central Luzon State University (3120), Science City of Mu˜noz, Nueva Ecija, Philippines

##### Abstract:

Let p and q be distinct primes. The semiprime divisor function graph denoted by GD(pq), is the graph with vertex set V(GD(pq)) = f1, p, q, pqg and edge set E(GD(pq)) = ff1, pg, f1, qg, f1, pqg, fp, pqg, fq, pqgg. The semiprime divisor function graph is a special type of divisor function graph GD(n) in which n = pq. Recently, the energy and some indices of semiprime divisor function graph have been determined. In this paper, we introduce a natural extension to the semiprime divisor function graph which we call the k-dprime divisor function graph. Moreover, we present results on some distance-based and degree-based topological indices of k-dprime divisor function graph. We end the paper by giving some open problems.

##### Keywords:

k-dprime divisor function graph, semiprime divisor function graph, divisor function graph, topological indices.

##### References:

- [1] J.A. Bondy, and U.S.R. Murty, Graph Theory, Springer, 2008. 2
- [2] D.M. Burton, Elementary Number Theory, Seventh Edition, The McGraw-Hill Companies, 2010. 2
- [3] G. Chartrand, R. Muntean, V. Saenpholphat and P. Zhang, Which graphs are divisor graphs?, Congr. Numer., 151 (2001), 189–200. 1
- [4] C. Frayer, Properties of Divisor Graphs, Rose-Hulman Undergraduate Mathematics Journal, 4(2) (2003), 1–10. 1
- [5] K. Kannan, D. Narasimhan, and S. Shanmugavelan, The graph of divisor function D(n), International Journal of Pure and Applied Mathematics, 102(3) (2015), 483–494. 1
- [6] D. Narasimhan, A. Elamparithi, and R. Vignesh, Connectivity, Independency and Colorability of Divisor Function Graph GD(n), International Journal of Engineering and Advanced Technology, 8(2S) (2018), 209–213. 1
- [7] S. Shanmugavelan, K.T. Rajeswari, and C. Natarajan, A note on indices of primepower and semiprime divisor function graph, TWMS J. App. and Eng. Math., 11(special issue) (2021), 51–62. 1
- [8] G.S. Singh, and G. Santhosh, Divisor graphs - I, Preprint. 1
- [9] Y.-P. Tsao, A simple research of divisor graphs, The 29th Workshop on Combinatorial Mathematics and Computation Theory. 1
- [10] L.A. Vinh, Divisor graphs have arbitrary order and size, AWOCA (2006). 1

##### Cite this article as:

- John Rafael M. Antalan, Jerwin G. De Leon, Regine P. Dominguez, On K-Dprime Divisor Function Graph, Communications in Combinatorics, Cryptography & Computer Science, 2021(1), PP.67–83, 2021
- Export citation to BibTeX