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Domination is an important factor in determining the robustness of a graph structure. A thorough examination of the graph’s topological structure is necessary for analyzing and examining it for various aspects. Understanding the stability of a chemical compound is a significant criterion in chemistry, which necessitates conducting numerous experimental tests. The domination number and power domination number are pivotal in defining a wide range of physical properties, which include physiochemical properties, thermodynamic properties, chemical activities, and biological activities. The one-pentagonal carbon nanocone (1-PCNC) is a member of the carbon nanocone family and has a structure similar to that of honeycomb networks, which are renowned for their robustness. In this paper, we find the domination number and power domination number of 1-PCNC by considering it as an ( m -1)-layered infinite graph.
Pandian et al. (Thu,) studied this question.