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Volume 7, Issue 4
Some Bounds for the Steiner-Harary Index of a Graph

B. Sarveshkumar, B. Chaluvaraju & M. C. Mahesh Kumar

DOI: 10.12150/jnma.2025.1446

J. Nonl. Mod. Anal., 7 (2025), pp. 1446-1460.

Published online: 2025-07

[An open-access article; the PDF is free to any online user.]

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  • Abstract

The Steiner distance for the set $S ⊆ V (G)$ would simply be the number of edges in the minimal subtree connecting them and is denoted as $d_G(S).$ The Steiner-Harary index is $SH_k(G),$ defined as the sum of the reciprocal of the Steiner distance for all subsets with $k$ vertices in $G.$ In this article, we calculate the exact value of $SH_k(G)$ for specific graphs and establish new best possible lower and upper bounds and characterization. Furthermore, we explore the relationship between $SH_k(G)$ and other graph indices based on Steiner distance.

  • Keywords

Harary index, Steiner index, Steiner-Harary index.

  • AMS Subject Headings

05C05, 05C07, 05C12, 05C38

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JNMA-7-1446, author = {Sarveshkumar , B.Chaluvaraju , B. and Kumar , M. C. Mahesh}, title = {Some Bounds for the Steiner-Harary Index of a Graph}, journal = {Journal of Nonlinear Modeling and Analysis}, year = {2025}, volume = {7}, number = {4}, pages = {1446--1460}, abstract = {

The Steiner distance for the set $S ⊆ V (G)$ would simply be the number of edges in the minimal subtree connecting them and is denoted as $d_G(S).$ The Steiner-Harary index is $SH_k(G),$ defined as the sum of the reciprocal of the Steiner distance for all subsets with $k$ vertices in $G.$ In this article, we calculate the exact value of $SH_k(G)$ for specific graphs and establish new best possible lower and upper bounds and characterization. Furthermore, we explore the relationship between $SH_k(G)$ and other graph indices based on Steiner distance.

}, issn = {2562-2862}, doi = {https://doi.org/10.12150/jnma.2025.1446}, url = {http://global-sci.org/intro/article_detail/jnma/24245.html} }
TY - JOUR T1 - Some Bounds for the Steiner-Harary Index of a Graph AU - Sarveshkumar , B. AU - Chaluvaraju , B. AU - Kumar , M. C. Mahesh JO - Journal of Nonlinear Modeling and Analysis VL - 4 SP - 1446 EP - 1460 PY - 2025 DA - 2025/07 SN - 7 DO - http://doi.org/10.12150/jnma.2025.1446 UR - https://global-sci.org/intro/article_detail/jnma/24245.html KW - Harary index, Steiner index, Steiner-Harary index. AB -

The Steiner distance for the set $S ⊆ V (G)$ would simply be the number of edges in the minimal subtree connecting them and is denoted as $d_G(S).$ The Steiner-Harary index is $SH_k(G),$ defined as the sum of the reciprocal of the Steiner distance for all subsets with $k$ vertices in $G.$ In this article, we calculate the exact value of $SH_k(G)$ for specific graphs and establish new best possible lower and upper bounds and characterization. Furthermore, we explore the relationship between $SH_k(G)$ and other graph indices based on Steiner distance.

Sarveshkumar , B.Chaluvaraju , B. and Kumar , M. C. Mahesh. (2025). Some Bounds for the Steiner-Harary Index of a Graph. Journal of Nonlinear Modeling and Analysis. 7 (4). 1446-1460. doi:10.12150/jnma.2025.1446
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