Strong metric dimensions for power graphs of finite groups

References

• Aalipour, G., Akbari, S., Cameron, P.J., Nikandish, R., Shaveisi, F. (2017). On the structure of the power graph and the enhanced power graph of a group. Electron. J. Combin. 24(3):P3.16. DOI: 10.37236/6497.
   Web of Science ®Google Scholar
• 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
• Anitha, T., Rajkumar, R. (2019). On the power graph and the reduced power graph of a finite group. Commun. Algebra 47(8):3329–3339. DOI: 10.1080/00927872.2018.1555842.
   Web of Science ®Google Scholar
• Anitha, T., Rajkumar, R. (2020). Characterization of groups with planar, toroidal or projective planar (proper) reduced power graphs. J. Algebra Appl. 19(5):2050099.
   Web of Science ®Google Scholar
• Bera, S., Bhuniya, A. K. (2018). On enhanced power graphs of finite groups. J. Algebra Appl. 17(08):1850146–1850148. DOI: 10.1142/S0219498818501463.
   Web of Science ®Google Scholar
• Bubboloni, D., Iranmanesh, M. A., Shaker, S. M. (2017). On some graphs associated with the finite alternating groups. Commun. Algebra 45(12):5355–5373. DOI: 10.1080/00927872.2017.1307381.
   Web of Science ®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
• Cameron, P. J., Guerra, H., Jurina, Š. (2019). The power graph of a torsion-free group. J. Algebr. Comb. 49(1):83–98. DOI: 10.1007/s10801-018-0819-1.
   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
• Costanzo, D. G., Lewis, M. L., Schmidt, S., Tsegaye, E., Udell, G. (2021). The cyclic graph (deleted enhanced power graph) of a direct product. Involve. 24:167–179. DOI: 10.2140/involve.2021.14.167.
   Google Scholar
• Costanzo, D. G., Lewis, M. L., Schmidt, S., Tsegaye, E., Udell, G. (2020). The cyclic graph of a Z-group. Bull. Aust. Math. Soc. (published online). DOI: 10.1017/s0004972720001318.
   Web of Science ®Google Scholar
• Deaconescu, M. (1989). Classification of finite groups with all elements of prime order. Proc. Am. Math. Soc. 106(3):625–629. DOI: 10.1090/S0002-9939-1989-0969518-2.
   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. Eur. J. Combin. 43:82–97. DOI: 10.1016/j.ejc.2014.08.019.
   Web of Science ®Google Scholar
• Gorenstein, D. (1980). Finite Groups. New York: Chelsea Publishing Co.
   Google Scholar
• Hamzeh, A., Ashrafi, A. R. (2017). Automorphism group of supergraphs of the power graph of a finite group. Eur. J. Combin. 60:82–88. DOI: 10.1016/j.ejc.2016.09.005.
   Web of Science ®Google Scholar
• Hamzeh, A., Ashrafi, A. R. (2018). The order supergraph of the power graph of a finite group. Turk. J. Math. 42(4):1978–1989. DOI: 10.3906/mat-1711-78.
   Web of Science ®Google Scholar
• Hamzeh, A., Ashrafi, A. R. (2019). Some remarks on the order supergraph of the power graph of a finite group. Int. Electron. J. Algebra. 26:1–12.
   Web of Science ®Google Scholar
• Harary, F., Melter, R. A. (1976). On the metric dimension of a graph. Ars Combin. 2:191–195 [Database].
   Google Scholar
• Higman, G. (1957). Finite groups in which every element has prime power order. J. Lond. Math. Soc. s1-32(3):335–342. DOI: 10.1112/jlms/s1-32.3.335.
   Google Scholar
• Johnson, D. L. (1980). Topics in the Theory of Group Presentations, London Math. Soc. Lecture Note Ser., Vol. 42. Cambridge, New York: Cambridge University Press.
   Google Scholar
• Kelarev, A. V. (2002). Ring Constructions and Applications. River Edge, NJ: World Scientific.
   Google Scholar
• Kelarev, A. V. (2003). Graph Algebras and Automata. New York: Marcel Dekker.
   Google Scholar
• Kelarev, A. V. (2004). Labelled Cayley graphs and minimal automata. Australas. J. Combin. 30:95–101.
   Google Scholar
• Kelarev, A. V., Quinn, S. J. (2000). A combinatorial property and power graphs of groups. Contrib. General Algebra 12:229–235.
   Google Scholar
• Kelarev, A. V., Ryan, J., Yearwood, J. (2009). Cayley graphs as classifiers for data mining: The influence of asymmetries. Discret. Math. 309(17):5360–5369. DOI: 10.1016/j.disc.2008.11.030.
   Web of Science ®Google Scholar
• Kratica, J., Kovačević-Vujčić, V., Čangalović, M., Mladenović, N. (2014). Strong metric dimension: A survey. Yugosl. J. Oper. Res. 24(2):187–198. DOI: 10.2298/YJOR130520042K.
   Google Scholar
• Kuziak, D., Yero, I. G., Rodríguez-Velázquez, J. A. (2015). On the strong metric dimension of the strong products of graphs. Open Math. 13:64–74.
   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
• Ma, X., She, Y. (2020). The metric dimension of the enhanced power graph of a finite group. J. Algebra Appl. 19(01):2050020. DOI: 10.1142/S0219498820500206.
   Web of Science ®Google Scholar
• Moghaddamfar, A. R., Rahbariyan, S., Shi, W. J. (2014). Certain properties of the power graph associated with a finite group. J. Algebra Appl. 13(07):1450040. DOI: 10.1142/S0219498814500406.
   Web of Science ®Google Scholar
• Ma, X., Walls, G. L., Wang, K. (2019). Power graphs of (non)orientable genus two. Commun. Algebra 47(1):276–288. DOI: 10.1080/00927872.2018.1476522.
   Web of Science ®Google Scholar
• Panda, R. P., Dalal, S., Kumar, J. (2021). On the enhanced power graph of a finite group. Commun. Algebra 49(4):1697–1716. DOI: 10.1080/00927872.2020.1847289.
   Web of Science ®Google Scholar
• Rajkumar, R., Anitha, T. (2017). Reduced power graph of a group. Electron. Notes Discrete Math. 63:69–76. DOI: 10.1016/j.endm.2017.10.063.
   Google Scholar
• Rajkumar, R., Anitha, T. (2021). Some results on the reduced power graph of a group. Southeast Asian Bull. Math. 45:241–262.
   Web of Science ®Google Scholar
• Sebő, A., Tannier, E. (2004). On metric generators of graphs. Math. OR. 29(2):383–393. DOI: 10.1287/moor.1030.0070.
   Web of Science ®Google Scholar
• Slater, P. J. (1975). Leaves of trees. Congr. Numer. 14:549–559.
   Google Scholar