Original Research Article

Article volume = 2021 and issue = 1

Pages: 67–83

Article publication Date: November, 1, 2021

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