Abstract
Given a connected (molecular) graph G, its Harary index H(G) is defined by the reciprocal sum of the distances between all unordered pairs of vertices of G. Lower bounds on the graph vulnerability parameters binding number and toughness have been often used to determine that the graph has a certain property. Recently, Yatauro [Discrete Appl. Math. 338 (2023) 56-68] gave a sharp upper bound of W(G) (Wiener index) to ensure that G has a determined lower bound (greater than or equal to 1) for the binding number or toughness. In this paper, we supply an upper bound on H(G) to ensure that G has a determined lower bound (between 0 and 1) for the binding number or toughness, and show that these bounds are best possible in some sense.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
