## Abstract

For a graph G without isolated vertices, the inverse degree of a graph G is defined as ID(G) = ∑_{u2V(G)} d(u)^{-1} where d(u) is the number of vertices adjacent to the vertex u in G. By replacing-1 by any non-zero real number we obtain zeroth-order general Randic index, i.e., 0R_{γ}(G) = ∑_{u2V(G)} d(u)^{γ}, where γ ∈ R-System. Text. UTF8Encoding. Xu et al. investigated some lower and upper bounds on ID for a connected graph γ in terms of connectivity, chromatic number, number of cut edges, and clique number. In this paper, we extend their results and investigate if the same results hold for γ < 0. The corresponding extremal graphs have also been identified.

Original language | English |
---|---|

Article number | 98 |

Journal | Mathematics |

Volume | 8 |

Issue number | 1 |

DOIs | |

Publication status | Published - Jan 1 2020 |

## Keywords

- Extremal graphs
- Graph parameters
- Inverse degree
- Zeroth order general Randic index

## ASJC Scopus subject areas

- Computer Science (miscellaneous)
- Engineering (miscellaneous)
- General Mathematics