2024/02/24 by An, Junfeng, Tian, Yingzhi
#Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.2402.15778
The Wiener index W(G) of a graph G is one of the most well-known topological indices, which is defined as the sum of distances between all pairs of vertices of G. The diameter D(G) of G is the maximum distance between all pairs of vertices of G; the conditional diameter D(G;s) is the maximum distance between all pairs of vertex subsets with cardinality s of G. When s=1, the conditional diameter D(G;s) is just the diameter D(G). The authors in \citeQS characterized the graphs with the maximum Wiener index among all graphs with diameter D(G)=n-c, where 1≤ c≤ 4. In this paper, we will characterize the graphs with the maximum Wiener index among all graphs with conditional diameter D(G;s)=n-2s-c ( -1≤ c≤ 1), which extends partial results in \citeQS.