Article
Version 1
This version is not peer-reviewed
Tightness of Harary Graphs
Version 1
: Received: 14 August 2024 / Approved: 15 August 2024 / Online: 16 August 2024 (08:37:26 CEST)
How to cite: Javan, A.; Moeini, A.; Shekaramiz, M. Tightness of Harary Graphs. Preprints 2024, 2024081217. https://doi.org/10.20944/preprints202408.1217.v1 Javan, A.; Moeini, A.; Shekaramiz, M. Tightness of Harary Graphs. Preprints 2024, 2024081217. https://doi.org/10.20944/preprints202408.1217.v1
Abstract
In the design of real-world networks, researchers evaluate various structural parameters to assess vulnerability, including connectivity, toughness, and tenacity. Recently, the tightness metric has emerged as a potentially superior vulnerability measure, although many related theorems remain unknown due to its novelty. Harary graphs, known for their maximum connectivity, are an important class of graph models for network design. Prior work has evaluated the vulnerability of three types of Harary graphs using different parameters, but the tightness metric has not been thoroughly explored. This article aims to calculate the tightness values for all three types of Harary graphs. First, it will attempt to calculate the lower bound for the value of the tightness parameter in Harary graphs using existing lemmas and theorems. Then, by presenting new lemmas and theorems, we will try to find the exact value or upper bound for this parameter in Harary graphs. For the first type of Harary graph, the tightness is precisely determined, while for the second and third types, upper bounds are provided due to structural complexity. The lemmas, theorems, and proof methods presented in this research may be used to calculate other graph and network parameters. However, the newness of the tightness parameter means that further research is needed to fully characterize its properties.
Keywords
Network Vulnerability; Tightness; Harary Graphs; Connectivity; Hamiltonian Circuit
Subject
Computer Science and Mathematics, Applied Mathematics
Copyright: This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Comments (0)
We encourage comments and feedback from a broad range of readers. See criteria for comments and our Diversity statement.
Leave a public commentSend a private comment to the author(s)
* All users must log in before leaving a comment