Brief survey on divisor graphs and divisor function graphs

References

• AbuHijleh, E. A., AbuGneim, O. A., Al-Ezeh, H. (2015). Divisor graphs and powers of trees. J. Comput. Sci. Comput. Math. 5: 61–66.
   Google Scholar
• Acharya, B. D., Hegde, S. M. (1990). Arithmetic graphs. J. Graph Theory 14: 275–299.
   Web of Science ®Google Scholar
• Ahmad, M., Al-Ezeh, H. (2018). Divisor graphs that are complements of bipartite graphs. J. Appl. Comput. Math. 7: 2.
   Google Scholar
• Al-Addasi, S., AbuGhneim, O. A., Al-Ezeh, H. (2010). Characterizing powers of cycles that are divisor graphs. Ars Combin. A 97:447–451.
   Google Scholar
• Al-Addasi, S., AbuGhneim, O. A., Al-Ezeh, H. (2012). Further new properties of divisor graphs. J. Comb. Math. Comb. Comput. 81: 261.
   Google Scholar
• Al-Addasi, S., AbuGhneim, O. A., Al-Ezeh, H. (2012). Line graphs and middle graphs that are divisor graphs. WSEAS Trans. Math. 19: 108–112.
   Google Scholar
• Anderson, D. D., Camillo, V. (1998). Armendariz rings and Gaussian rings. Commun. Algebra. 26: 2265–2272.
   Web of Science ®Google Scholar
• Antalan, J. R. M., De Leon, J. G., Dominguez, R. (2021). On k-dprime divisor function graph. arXiv preprint arXiv:2111.02183.
   Google Scholar
• Aravinth, R. H., Vignesh, R. (2019). Mobius function graph Mn(G). Int. J. Innov. Technol. Exploring Eng. 8: 1481–1484.
   Google Scholar
• Berrizbeitia, P., Berrizbeitia, R. E. (1996). Counting pure kcycles in sequences of Cayley graphs. Discrete Math. 149: 11–18.
   Web of Science ®Google Scholar
• Chalapathi, T., Madhavi, L., Venkataramana, S. (2013). Enumeration of triangles in a divisor Cayley graph. Momona Ethiopian J. Sci. 5: 163–173.
   Google Scholar
• Chartrand, G., Muntean, R., Saenpholphat, V., Zhang, P. (2001). Which graphs are divisor graphs? Congr. Numer. 151: 189–200.
   Google Scholar
• De Bruijn, N. G. (1951). On the number of positive integers >x and free of prime factors >y. Nederl. Akad. Wetensch. Proc. Ser. A 54: 50–60.
   Google Scholar
• Dejter, I. J., Giudici, R. E. (1995). On unitary Cayley graphs. J. Combin. Math. Combin. Comput. 18: 121–124.
   Google Scholar
• Erdös, P., Freud, R., Hegyári, N. (1983). Arithmetical properties of permutations of integers. Acta Math. Hungarica. 41: 169–176.
   Web of Science ®Google Scholar
• Frayer, C. (2003). Properties of divisor graphs. Rose-Hulman Undergraduate Math. J. 4: 4.
   Google Scholar
• Friedlander, J. B. (1976). Integers free from large and small primes. Proc. London Math. Soc. 3: 565–576.
   Google Scholar
• Iranmanesh, M. A., Praeger, C. E. (2010). Bipartite divisor graphs for integer subsets. Graphs Comb. 26: 95–105.
   Web of Science ®Google Scholar
• Kannan, K., Narasimhan, D., Shanmugavelan, S. (2015). The graph of divisor function D(n). Int. J. Pure Appl. Math. 102: 483–494.
   Google Scholar
• V M S S Kiran Kumar, R., Chalapathi, T. (2018). Difference divisor graph of the finite group. Int. J. Res. Ind. Eng. 7: 235–242.
   Google Scholar
• Madhavi, L., Chalapathi, T. (2015). Enumeration of triangles in Cayley graphs. Pure Appl. Math. J. 4: 128–132.
   Google Scholar
• Mirona, G., Maheswari, B. (2015). Dominating sets of divisor Cayley graphs. Int. J. Sci. & Eng. Res. 6: 119–128.
   Google Scholar
• Nair, S. M., Kumar, J. S. (2022). Divisor prime graph. J. Math. Comput. Sci. 12: Article ID: 112.
   Google Scholar
• Narasimhan, D., Elamparithi, A., Vignesh, R. (2018). Connectivity, independency and colorability of divisor function graph GD(n). Int. J. Eng. Adv. Technol. 8: 209–213.
   Google Scholar
• Narasimhan, D., Vignesh, R., Elamparithi, A. (2018). Directed divisor function graph GDij(n). Int. J. Eng. Adv. Technol. 8: 214–218.
   Google Scholar
• Nathanson, M. B. (1980). Connected components of arithmetic graphs. Monatsh. für Math. 89: 219–222.
   Web of Science ®Google Scholar
• Osba, E. A., Alkam, O. (2017). When zero-divisor graphs are divisor graphs. Turk. J. Math. 41: 797–807.
   Web of Science ®Google Scholar
• Pollington, A. D. (1983). There is a long simple path in the divisor graph. Ars Combin. A. 16: 303–304.
   Google Scholar
• Pomerance, C. (1983). On the longest simple path in the divisor graph. Congr. Numer. 40: 291–304.
   Google Scholar
• Shanmugavelan, S., Rajeswari, K. T., Chidambaram, N. (2021). A note on indices of primepower and semiprime divisor function graph. TWMS J. Appl. Eng. Math. 11: 51–62.
   Web of Science ®Google Scholar
• Singh, G. S., Santhosh, G. (2006). Divisor Graphs - I. preprint.
   Google Scholar
• Sujatha, K., Nagamuni R. L. (2008). Studies on domination parameters and cycle structure of cayley graphs associated with some arithmetical functions. Ph.D. Thesis, Sri Venkateswara University, Tirupati, India.
   Google Scholar
• Tsao, Y. P. (2012). A simple research of divisor graphs. In: The ${29}^{th}$ Workshop on Combinatorial Mathematics and Computation Theory, pp. 186–190.
   Google Scholar
• Vasumathi, N. (1994). Graphs on Numbers. Ph.D. Thesis, Sri Venkateswara University, Tirupati, India.
   Google Scholar
• Vinh, L. A. (2006). Divisor graphs have arbitrary order and size. arXiv preprint math/0606483.
   Google Scholar