Nordhaus–gaddum-type results for the steiner gutman index of graphs

Zhao Wang, Yaping Mao, Kinkar Chandra Das*, Yilun Shang

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

9 Citations (Scopus)
45 Downloads (Pure)


Building upon the notion of the Gutman index SGut(G), Mao and Das recently introduced the Steiner Gutman index by incorporating Steiner distance for a connected graph G. The Steiner Gutman k-index SGutk (G) of G is defined by SGutk (G) = ∑S⊆V(G),|S|=k (∏v∈S degG (v)) dG (S), in which dG (S) is the Steiner distance of S and degG (v) is the degree of v in G. In this paper, we derive new sharp upper and lower bounds on SGutk, and then investigate the Nordhaus-Gaddum-type results for the parameter SGutk . We obtain sharp upper and lower bounds of SGutk (G) + SGutk (G) and SGutk (G) · SGutk (G) for a connected graph G of order n, m edges, maximum degree ∆ and minimum degree δ.

Original languageEnglish
Article number1711
Number of pages14
Issue number10
Publication statusPublished - 16 Oct 2020


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