Reduced First Zagreb Index of Graphs with Added Edges
Proceedings of the Jangjeon Mathematical Society, vol.29, no.3, pp.527-536, 2026 (Scopus)
- Publication Type: Article / Article
- Volume: 29 Issue: 3
- Publication Date: 2026
- Doi Number: 10.17777/pjms2026.29.3.005
- Journal Name: Proceedings of the Jangjeon Mathematical Society
- Journal Indexes: Scopus, MathSciNet, zbMATH
- Page Numbers: pp.527-536
- Keywords: edge addition, graph index, Graphs, pendant edge, reduced first Zagreb index, vertex degrees
- Bursa Uludag University Affiliated: Yes
Abstract
Adding or deleting an edge or a vertex gives a larger or smaller graph compared to the original graph and hence the calculations on the smaller graph helps us to get the information on larger graph. In network theory, adding or deleting a member affects many things within the network including the strength of it. In this paper, we compute the change in the reduced first Zagreb index of a simple graph G when an arbitrary edge is added. In particular, some state-ments for the change of reduced first Zagreb indices of path, cycle, star, complete, complete bipartite and tadpole graphs are obtained.