In quantitative structure-property relationship (QSPR) and quantitative structure-activity relationship (QSAR) studies, computation of topological indices is a vital tool to predict biochemical and physio-chemical properties of chemical structures. Numerous topological indices have been inaugurated to describe different topological features. The ev and ve-degree are recently introduced novelties, having stronger prediction ability. In this article, we derive formulae of the ev-degree and ve-degree based topological indices for chemical structure of _{2}_{3} −

Researchers have found applications of graph theory and topological models in various scientific research fields during last decades. Theoretical physics, toxicology, computer sciences, pharmacology, pharmaceutical chemistry, engineering and architecture are diverse areas utilizing graph theory and models to make numerous improvements in existing scientific literature [

TIs assist in the course of investigation and prediction of the physio-chemical and biochemical properties,

Silicon, the second most abundant element on earth, has unique physical and chemical properties due to its semi-conductance and nontoxic nature. Silicon carbides has diverse industrial applications because of thermal and chemical stability, high erosion resistance, high melting point, non oxidizing behavior [

The main objective of the article is to derive formulae to calculate the ev-degree and ve-degree based TIs for _{2}_{3} −

Let _{ev}(_{ve}(

The first ve-degree based Zagreb alpha index is as follows:

The first ve-degree based Zagreb beta index is defined as:

The second ve-degree based Zagreb index is given by the formula:

The ve-degree based Randíc index is as follows:

The ev-degree based Randíc index is defined as:

The ve-degree based atom-bond connectivity index is given by the formula:

The ve-degree based geometric-arithmetic index is as follows:

The ve-degree based harmonic index is defined as:

The ve-degree based sum-connectivity index is given by the formula:

We compute these indices by using the vertex partition strategy, the edge partition techniques, expository strategies, sum of degrees of neighboring techniques, degree checking and combinatorial techniques. We use Matlab and Maple for some calculations and verification purpose.

Consider the two dimensional molecular structure of _{2}_{3} −

Total Vertices | 10 |
---|---|

Total Edges | 15 |

Number of vertex | |
---|---|

1 | 2 |

2 | 4 |

3 | 10 |

•

To compute the ev-degree based Zagreb index of _{2}_{3} −

(_{1}), _{2})) |
Number of edges |
---|---|

(1,2) | 1 |

(1,3) | 1 |

(2,2) | |

(2,3) | 6 |

(3,3) | 15 |

•

To compute the first ve-degree based zagreb alpha index of _{2}_{3} −

Number of vertices | ||
---|---|---|

1 | 2 | 1 |

1 | 3 | 1 |

2 | 4 | 2 |

2 | 5 | 2 |

2 | 6 | 2 |

3 | 5 | 1 |

3 | 6 | |

3 | 7 | |

3 | 8 | 2 |

3 | 9 | 10 |

•

To compute first ve-degree based Zagreb beta index of _{2}_{3} −

(_{1}), _{2})) |
Number of edges | |
---|---|---|

(1,2) | (2,4) | 1 |

(1,3) | (3,5) | 1 |

(2,2) | (4,5) | 2 |

(5,5) | ||

(2,3) | (4,6) | |

(4,7) | ||

(5,5) | ||

(5,6) | ||

(5,7) | ||

(5,8) | ||

(6,7) | ||

(6,8) | ||

(3,3) | (7,7) | |

(7,8) | ||

(7,9) | ||

(8,8) | ||

(8,9) | ||

(9,9) |

•

To compute the second ve-degree based Zagreb index of _{2}_{3} −

•

To compute the ve-degree based Randíc index of _{2}_{3} −

•

To compute the ev-degree based Randíc index of _{2}_{3} −

(_{1}), _{2})) |
Number of edges | |
---|---|---|

(1,2) | 3 | 1 |

(1,3) | 4 | 1 |

(2,2) | 4 | |

(2,3) | 5 | 6 |

(3,3) | 6 | 15 |

•

To compute the ve-degree based atom-bond connectivity index of _{2}_{3} −

•

To compute the ve-degree based geometric-arithmetic index of _{2}_{3} −

•

To compute the ve-degree based harmonic index of _{2}_{3} −

•

To compute the ve-degree based sum-connectivity index of _{2}_{3} −

In this section, we present the graphical analysis of the computed topological indices for _{2}_{3} −

In this article, we have provided results related to the ve-degree Zagreb alpha index, first ve-degree Zagreb beta index, second ve-degree Zagreb index, ve-degree Randíc index, ev-degree Randíc index, ve-degree atom-bond connectivity index, ve-degree geometric-arithmetic index, ve-degree harmonic index and ve-degree sum-connectivity index for the two dimensional molecular structure of _{2}_{3} −

The

All the authors are thankful to their respective institutes.