## Abstract

The general Randić index of a graph G is defined as R_{α}(G) = Σ_{uv∈E(G)}(d_{u}d_{v})^{α}, where du and dv denote the degrees of the vertices u and v, respectively, α is a real number, and E(G) is the edge set of G. The minimum number of edges of a graph G whose removal makes G as acyclic is known as the cyclomatic number and it is usually denoted by ν. A graph with the maximum degree at most 4 is known as a chemical graph. For ν = 0, 1, 2 and α > 1, the problem of finding graph(s) with the minimum general Randić index R_{α} among all n-vertex chemical graphs with the cyclomatic number ν has already been solved. In this paper, this problem is solved for the case when ν ≥ 3, n ≥ 5(ν - 1), and 1 < α < α0, where α_{0} ≈ 11.4496 is the unique positive root of the equation 4(8^{α} - 6^{α}) + 4^{α} - 9^{α} = 0.

Original language | English |
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Pages (from-to) | 113-122 |

Number of pages | 10 |

Journal | Mathematical Reports |

Volume | 25-75 |

Issue number | 1 |

DOIs | |

State | Published - 2023 |

### Bibliographical note

Publisher Copyright:© 2023 Editura Academiei Romane. All rights reserved.

## Keywords

- Randić index
- cyclomatic number
- extremal problem
- general Randić index
- topological index

## ASJC Scopus subject areas

- Analysis
- Algebra and Number Theory
- Geometry and Topology
- Applied Mathematics