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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Official URL: https://doi.org/10.3390/sym12101711

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.

Item Type: Article
Uncontrolled Keywords: Distance; Steiner distance; Gutman index; Steiner Gutman k-index
Subjects: G400 Computer Science
Department: Faculties > Engineering and Environment > Computer and Information Sciences
Depositing User: Elena Carlaw
Date Deposited: 05 Nov 2020 15:30
Last Modified: 05 Nov 2020 15:30
URI: http://nrl.northumbria.ac.uk/id/eprint/44695

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