Sharp Inequalities for the Generalized Steiner-Gutman Index

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Published: Mar 15, 2025
Keywords:
Wiener index, Steiner index, Steiner gutman index

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B. Sarveshkumar
Department of Mathematics, Bangalore University, Jnana Bharathi Campus, Bangalore -560 056, India
B. Chaluvaraju
Department of Mathematics, Bangalore University, Jnana Bharathi Campus, Bangalore -560 056, India

Abstract

For any connected graph  with real numbers ,  and a positive integer , the Steiner distance is denoted by  for a set of vertices  is defined as the minimum size of connected subgraphs that include a given set of vertices  with . In this article, we introduce a new version of the Steiner-Gutman index for a graph , defined it as


 


where  and  are any real numbers. In this paper, we obtained some best possible inequalities and their characterizations in terms of the order, size, minimum / maximum degree, and diameter of . Also, the comparisons of  with other graphical indices are obtained.

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B. Sarveshkumar, B. Chaluvaraju. Sharp Inequalities for the Generalized Steiner-Gutman Index . J. Int. Acad. Phys. Sci. [Internet]. 2025 Mar. 15 [cited 2025 May 16];29(1):1-12. Available from: https://www.iaps.org.in/journal/index.php/journaliaps/article/view/696
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Vol. 29 No. 1 (2025): Table of Content
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