Structural analysis of transformations of subdivision graph via structure descriptors

Abstract

For a graph X=(V(X),E(X)), a wide range of transformations are possible. A graph X can be converted into a new graph by adding vertices or edges following certain criteria. A graph derived from the parent graph X by inserting a new vertex into each of its edge is known as subdivision graph and can be denoted as S(X). The transformation graph of a graph X can be defined as a graph whose vertex set is union of the vertex set and edge set of X and whose edge set is defined under certain conditions. Structure descriptors are widely used now-a-days to model the physico-chemical, structural and electronic properties of chemical compounds and networks. A structure descriptor of a transformation graph reflects different structural features than a structure descriptor of the original graph X. By determining various structure descriptors of the transformation graphs of a molecule, wide range of structural properties of the underlying molecule could be modelled. In this study, the concept of transformation graph is applied on subdivision graph and further the structural properties of those graphs are studied via structure descriptors. The expressions for first Zagreb index and forgotten index of transformation graphs of subdivision graphs are determined in terms of parameters of the parental graph. Further, applying the determined results, a structural analysis was also carried out on a chemical graph.

Keywords

• Subdivision graph
• Transformation graphs
• Total transformations
• Semi-total transformations
• Structural analysis
• Structure descriptors