Abstract
Chemical structural formula can be represented by chemical graphs in which atoms are considered as vertices and bonds between them are considered as edges. A topological index is a real value that is numerically obtained from a chemical graph to predict its various physical and chemical properties. Thorn graphs are obtained by attaching pendant vertices to the different vertices of a graph under certain conditions. In this paper, a numerical relation between the Gutman connection (GC) index of a graph and its thorn graph is established. Moreover, the obtained result is also illustrated by computing the GC index for the particular families of the thorn graphs such as thorn paths, thorn rods, thorn stars, and thorn rings.
Highlights
topological index (TI) are used in chemoinformatics which is combination of the three different subjects such as information science, chemistry, and mathematics
On the bases of quantitative structural activity relationship (QSAR) and the qualitative structural property relationship (QSPR), the different chemical properties of a chemical graph are correlated with its structure [3, 4]
Gutman and Trinajstic [5] evaluated the total π-electron energy of the molecular structure by using the sum of square of degree of vertices of molecular graphs that is known by first Zagreb index nowadays
Summary
TIs are used in chemoinformatics which is combination of the three different subjects such as information science, chemistry, and mathematics. Gutman and Trinajstic [5] evaluated the total π-electron energy of the molecular structure by using the sum of square of degree (number of neighborhoods) of vertices of molecular graphs that is known by first Zagreb index nowadays. Another descriptor appeared that is called as second Zagreb index. In 2018, Ali and Trinajstic [8] established a descriptor known as modified first Zagreb connection index. They presented two more descriptors with the name first and second Zagreb connection indices. In 1947, Wiener [14] first time applied a distance-based TI to find the boiling point of paraffin It is called as the Wiener index. E study of thorn graphs provides mathematical results that relate numerical values of TIs of plerograms and kenograms.
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