# Wiener index and Harary index on pancyclic graphs

## TL;DR

This paper explores conditions involving Wiener and Harary indices, as well as spectral properties, that guarantee a graph is pancyclic, extending previous spectral-based criteria for such graphs.

## Contribution

It introduces new sufficient conditions for pancyclicity based on Wiener index, Harary index, and spectral radii, broadening the understanding of graph properties related to cycles.

## Key findings

- Established conditions linking Wiener and Harary indices to pancyclicity.
- Connected spectral radii with topological indices to characterize pancyclic graphs.
- Extended previous spectral conditions by incorporating distance-based indices.

## Abstract

Wiener index and Harary index are two classic and well-known topological indices for the characterization of molecular graphs. Recently, Yu et al. \cite{YYSX} established some sufficient conditions for a graph to be pancyclic in terms of the edge number, the spectral radius and the signless Laplacian spectral radius of the graph. In this paper, we give some sufficient conditions for a graph being pancyclic in terms of the Wiener index, the Harary index, the distance spectral radius and the Harary spectral radius of a graph.