Original Research Article

Article volume = 2021 and issue = 1

Pages: 67–83

Article publication Date: November, 1, 2021

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# 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.

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