Year: 2023
Type: article
Abstract: Several measures of peripherality for vertices and edges in networks are investigated.Asymptotic bounds are improved on the maximum value achieved by the (i) edge peripherality over connected n-vertex graphs, (ii) edge sum peripherality over connected n-vertex graphs, (iii) edge sum peripherality over n-vertex graphs with diameter at most 2, (iv) edge sum peripherality over bipartite n-vertex graphs with diameter at most 3, and (v) Trinajstić index over n-vertex graphs.The maximum value achieved by the peripherality index over connected n-vertex graphs and n-vertex trees is also computed for all 1 ≤ n ≤ 8. Two conjectures of Furtula are refuted; the first one is on necessary conditions for minimizing the Trinajstić index and the second one is about maximizing the Trinajstić index.Finally, an asymptotic expression for the expected value of the irregularity of the random graph Gn,p is found for arbitrary p satisfying 0 < p < 1.
Source: Discrete Mathematics Letters
Author: Tang, Linus
Institution: Massachusetts Institute of Technology
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: diamond
OpenAlex ID: W4390044534