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Open AccessArticle

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

1
College of Science, China Jiliang University, Hangzhou 310018, Zhejiang, China
2
Department of Mathematics, Qinghai Normal University, Xining 810008, Qinghai, China
3
Center for Mathematics and Interdisciplinary Sciences of Qinghai Province, Xining 810008, Qinghai, China
4
Department of Mathematics, Sungkyunkwan University, Suwon 16419, Korea
5
Department of Computer and Information Sciences, Northumbria University, Newcastle NE1 8ST, UK
*
Authors to whom correspondence should be addressed.
Symmetry 2020, 12(10), 1711; https://doi.org/10.3390/sym12101711
Received: 18 September 2020 / Revised: 11 October 2020 / Accepted: 12 October 2020 / Published: 16 October 2020
(This article belongs to the Special Issue Analytical and Computational Properties of Topological Indices)
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)=SV(G),|S|=kvSdegG(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 Δ and minimum degree δ. View Full-Text
Keywords: distance; Steiner distance; Gutman index; Steiner Gutman k-index distance; Steiner distance; Gutman index; Steiner Gutman k-index
MDPI and ACS Style

Wang, Z.; Mao, Y.; Das, K.C.; Shang, Y. Nordhaus–Gaddum-Type Results for the Steiner Gutman Index of Graphs. Symmetry 2020, 12, 1711.

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