On the minimum degree of power graphs of finite nilpotent groups

References

• Abawajy, J., Kelarev, A., Chowdhury, M. (2013). Power graphs: a survey. Electron. J. Graph Theory Appl. 1(2):125–147. DOI: 10.5614/ejgta.2013.1.2.6.
   Google Scholar
• Burton, D. M. (2007). Elementary Number Theory, 6th ed. New Delhi, India: Tata McGraw-Hill Education.
   Google Scholar
• Cameron, P. J., Ghosh, S. (2011). The power graph of a finite group. Discrete Math. 311(13):1220–1222. DOI: 10.1016/j.disc.2010.02.011.
   Web of Science ®Google Scholar
• Chakrabarty, I., Ghosh, S., Sen, M. K. (2009). Undirected power graphs of semigroups. Semigroup Forum. 78(3):410–426. DOI: 10.1007/s00233-008-9132-y.
   Web of Science ®Google Scholar
• Chattopadhyay, S., Patra, K. L., Sahoo, B. K. (2019). Vertex connectivity of the power graph of a finite cyclic group. Discrete Appl. Math. 266:259–271. DOI: 10.1016/j.dam.2018.06.001.
   Web of Science ®Google Scholar
• Chattopadhyay, S., Patra, K. L., Sahoo, B. K. (2021). Minimal cut-sets in the power graphs of certain finite non-cyclic groups. Commun. Algebra 49(3):1195–1211. DOI: 10.1080/00927872.2020.1831005.
   Web of Science ®Google Scholar
• Curtin, B., Pourgholi, G. R. (2016). An Euler totient sum inequality. J. Number Theory. 163:101–113. DOI: 10.1016/j.jnt.2015.11.012.
   Web of Science ®Google Scholar
• Doostabadi, A., Ghouchan, M. F. D. (2015). On the connectivity of proper power graphs of finite groups. Commun. Algebra 43(10):4305–4319. DOI: 10.1080/00927872.2014.945093.
   Web of Science ®Google Scholar
• Feng, M., Ma, X., Wang, K. (2015). The structure and metric dimension of the power graph of a finite group. European J. Combin. 43:82–97. DOI: 10.1016/j.ejc.2014.08.019.
   Web of Science ®Google Scholar
• Plesník, J. (1975). Critical graphs of given diameter. Acta Fac. Rerum Natur. Univ. Comenian. Math. 30:71–93.
   Google Scholar
• Kelarev, A. V., Quinn, S. J. (2000). A combinatorial property and power graphs of groups. In Contributions to General Algebra, Vol. 12 (Vienna, 1999), Heyn, Klagenfurt, p. 229–235.
   Google Scholar
• Kirkland, S., Moghaddamfar, A. R., Navid Salehy, S., Nima Salehy, S., Zohourattar, M. (2018). The complexity of power graphs associated with finite groups. Contrib. Discrete Math. 13(2):124–136.
   Web of Science ®Google Scholar
• Kumar, A., Selvaganesh, L., Cameron, P. J., Tamizh Chelvam, T. (2021). Recent developments on the power graph of finite groups—a survey. AKCE Int. J. Graphs Comb. 18(2):65–94. DOI: 10.1080/09728600.2021.1953359.
   Web of Science ®Google Scholar
• Ma, X., Feng, M. (2015). On the chromatic number of the power graph of a finite group. Indag. Math. (N.S.). 26(4):626–633. DOI: 10.1016/j.indag.2015.04.003.
   Web of Science ®Google Scholar
• Ma, X., Feng, M., Wang, K. (2018). The strong metric dimension of the power graph of a finite group. Discrete Appl. Math. 239:159–164. DOI: 10.1016/j.dam.2017.12.021.
   Web of Science ®Google Scholar
• Mehranian, Z., Gholami, A., Ashrafi, A. R. (2017). The spectra of power graphs of certain finite groups. Linear Multilinear Algebra 65(5):1003–1010. DOI: 10.1080/03081087.2016.1221375.
   Web of Science ®Google Scholar
• Panda, R. P. (2019). Laplacian spectra of power graphs of certain finite groups. Graphs Combin. 35(5):1209–1223. DOI: 10.1007/s00373-019-02070-x.
   Web of Science ®Google Scholar
• Panda, R. P., Krishna, K. V. (2018). On the minimum degree, edge-connectivity and connectivity of power graphs of finite groups. Commun. Algebra 46(7):3182–3197. DOI: 10.1080/00927872.2017.1407424.
   Web of Science ®Google Scholar
• Panda, R. P., Patra, K. L., Sahoo, B. K. (2021). Characterizing finite nilpotent groups associated with a graph theoretic equality. Ric. Mat. DOI: 10.1007/s11587-021-00655-4.
   Google Scholar
• Panda, R. P., Patra, K. L., Sahoo, B. K. (2021). On the minimum degree of the power graph of a finite cyclic group. J. Algebra Appl. 20(3):2150044, 18pp. DOI: 10.1142/S0219498821500444.
   Web of Science ®Google Scholar
• Shitov, Y. (2017). Coloring the power graph of a semigroup. Graphs Combin. 33(2):485–487. DOI: 10.1007/s00373-017-1773-8.
   Web of Science ®Google Scholar