On ABS index of unicyclic graphs with fixed diameter
Given a simple connected graph G = (V(G), E(G)), the atom-bond sum-connectivity (ABS) index is defined as ABS(G)=?uv?E(G) ?d(u)+d (v)- 2/d(u)+d(v)=?uv?E(G)?1-2/d(u)+ d(v)', where d(u) and d(v) are the degrees of u, v ? V(G), respectively. In this paper, let Un,? be a set of all unicyclic graphs of order n with diameter ?. Firstly, we present the minimum ABS index of G ? Un,? with ? ? 2. We also determine the maximum ABS index of G ? Un,? with ? ? 4. Finally, the corresponding extremal graphs with the sharp upper and lower bounds have been characterized, respectively.
Authors
- Haiying Wang (ORCID: https://orcid.org/0000-0002-2058-5443)
- Shaohui Wang (ORCID: https://orcid.org/0000-0001-6941-3194)
- Yuan Zhang (ORCID: https://orcid.org/0009-0005-6262-9108)
Institutions
- China University of Geosciences (Beijing) (CN)
- Louisiana Christian University (US)
Publication Details
- Journal
- Filomat
- Published
- 2025-01-01
- DOI
- https://doi.org/10.2298/fil2504311z
- Citations
- 1
- Primary Topic
- Graph theory and applications
- Type
- article
- Field-Weighted Citation Impact
- 4.09
Funders
- China University of Geosciences, Beijing
- China University of Geosciences
- Division of Graduate Education