Steiner Gutman index

Yaping Mao; Kinkar Ch Das

Steiner Gutman index

Yaping Mao
, Kinkar Ch Das

Department of Mathematics

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

29 Scopus citations

Abstract

The concept of Gutman index SGut(G) of a connected graph G was introduced in 1994. The Steiner distance in a graph, introduced by Chartrand et al. in 1989, is a natural generalization of the concept of classical graph distance. In this paper, we generalize the concept of Gutman index by Steiner distance. The Steiner Gutman k-index SGut_k(G) of G is defined by SGut_k(G) = (Equestion presented), where d_G(S) is the Steiner distance of S and deg_G(v) is the degree of v in G. Expressions for SGut_k for some special graphs are obtained. We also give sharp upper and lower bounds of SGut_k of a connected graph, and get the expression of SGut_k(G) for k = n, n - 1. Finally, we compare between k-center Steiner degree distance SDD_k and SGut_k of graphs.

Original language	English
Pages (from-to)	779-794
Number of pages	16
Journal	Match
Volume	79
Issue number	3
State	Published - 2018

Cite this

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title = "Steiner Gutman index",

abstract = "The concept of Gutman index SGut(G) of a connected graph G was introduced in 1994. The Steiner distance in a graph, introduced by Chartrand et al. in 1989, is a natural generalization of the concept of classical graph distance. In this paper, we generalize the concept of Gutman index by Steiner distance. The Steiner Gutman k-index SGutk(G) of G is defined by SGutk(G) = (Equestion presented), where dG(S) is the Steiner distance of S and degG(v) is the degree of v in G. Expressions for SGutk for some special graphs are obtained. We also give sharp upper and lower bounds of SGutk of a connected graph, and get the expression of SGutk(G) for k = n, n - 1. Finally, we compare between k-center Steiner degree distance SDDk and SGutk of graphs.",

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year = "2018",

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AU - Mao, Yaping

AU - Das, Kinkar Ch

PY - 2018

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AB - The concept of Gutman index SGut(G) of a connected graph G was introduced in 1994. The Steiner distance in a graph, introduced by Chartrand et al. in 1989, is a natural generalization of the concept of classical graph distance. In this paper, we generalize the concept of Gutman index by Steiner distance. The Steiner Gutman k-index SGutk(G) of G is defined by SGutk(G) = (Equestion presented), where dG(S) is the Steiner distance of S and degG(v) is the degree of v in G. Expressions for SGutk for some special graphs are obtained. We also give sharp upper and lower bounds of SGutk of a connected graph, and get the expression of SGutk(G) for k = n, n - 1. Finally, we compare between k-center Steiner degree distance SDDk and SGutk of graphs.

UR - https://www.scopus.com/pages/publications/85043506826

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AN - SCOPUS:85043506826

SN - 0340-6253

VL - 79

SP - 779

EP - 794

JO - Match

JF - Match

IS - 3

ER -

Steiner Gutman index

Abstract

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