Nordhaus–Gaddum-Type Results for the Steiner Gutman Index of Graphs

Wang, Zhao, Mao, Yaping, Das, Kinkar Chandra and Shang, Yilun (2020) Nordhaus–Gaddum-Type Results for the Steiner Gutman Index of Graphs. Symmetry, 12 (10). p. 1711. ISSN 2073-8994

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Abstract

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.

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