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

Zhao Wang; Yaping Mao; Kinkar Chandra Das; Yilun Shang

doi:10.3390/sym12101711

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

School of Computer Science

Research output: Contribution to journal › Article › peer-review

10 Citations (Scopus)

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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 SGut_k (G) of G is defined by SGut_k (G) = ∑_S_{⊆V(G),|S|=k} (∏_v_∈S deg_G (v)) d_G (S), in which d_G (S) is the Steiner distance of S and deg_G (v) is the degree of v in G. In this paper, we derive new sharp upper and lower bounds on SGut_k, and then investigate the Nordhaus-Gaddum-type results for the parameter SGut_k . We obtain sharp upper and lower bounds of SGut_k (G) + SGut_k (G) and SGut_k (G) · SGut_k (G) for a connected graph G of order n, m edges, maximum degree ∆ and minimum degree δ.

Original language	English
Article number	1711
Number of pages	14
Journal	Symmetry
Volume	12
Issue number	10
DOIs	https://doi.org/10.3390/sym12101711
Publication status	Published - 16 Oct 2020

Keywords

Distance
Gutman index
Steiner distance
Steiner Gutman k-index

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10.3390/sym12101711Licence: CC BY

symmetry-12-01711-v2Final published version, 291 KBLicence: CC BY

Cite this

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title = "Nordhaus–gaddum-type results for the steiner gutman index of graphs",

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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author = "Zhao Wang and Yaping Mao and Das, \{Kinkar Chandra\} and Yilun Shang",

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AU - Wang, Zhao

AU - Mao, Yaping

AU - Das, Kinkar Chandra

AU - Shang, Yilun

PY - 2020/10/16

Y1 - 2020/10/16

N2 - 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.

AB - 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.

KW - Distance

KW - Gutman index

KW - Steiner distance

KW - Steiner Gutman k-index

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VL - 12

JO - Symmetry

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ER -

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

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Keywords

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